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This study introduces a design of robust finite-time controllers that aims to solve the trajectory tracking of robot manipulators with full-state constraints. The control design is based on the construction of a distributed state constraint non-singular terminal sliding mode (CNTSM). The CNTSM design includes the gain self-adapting tuning method, which can ensure finite-time convergence to the sliding surface aside from the states to its corresponding reference trajectories. The implementation of the time-varying gain ensures the fulfillment of the accurate tracking for the references while the position and velocity constraints are satisfied permanently. A barrier Lyapunov function is proposed to develop the finite-time stability analysis of the designed controllers. The CNTSM realization uses the tracking error as well as its estimated derivative, which is calculated using a variant of adaptive super-twisting algorithm operating as robust differentiator. The proposed CNTSM is numerically evaluated on a two-link RM with uncertain inertia and Coriolis matrices. Simulation and experimental results evidence the efficiency of the CNTSM controller demonstrating a better tracking performance while the full-state constraints are satisfied in counterpart with the classical non-singular terminal sliding mode which is not able to keep such restrictions.

This study describes the design, instrumentation and control of an exoskeleton for lower limb children rehabilitation with nine degrees of freedom. Three degrees of freedom in each leg exert the movements of hip, knee and ankle in the sagittal plane, and three control the drive track system composed by a caterpillar-like robot. The control scheme presents a model free decentralized output feedback adaptive high-order sliding mode control to solve the trajectory tracking problem in each degree of freedom of the exoskeleton. A high order sliding mode differentiator estimates the unmeasured states and, by means of a dynamical state extension, it approximates the unknown dynamical model of the exoskeleton. A second-order adaptive sliding mode controller based on the super-twisting algorithm drives the exoskeleton articulations to track the proposed reference trajectories, inducing an ultimate boundedness for the tracking error. Numerical and experimental simulation results demonstrate the effect of the adaptive gain on the super-twisting control design. Such evaluations confirmed the superior tracking performance forced by the adaptive law for the controller with a smaller chattering amplitude and smaller mean tracking error.

A drum boiler is the most critical part of power generation plants. The control of a highly nonlinear, multiple input and multiple output drum boiler system (DBS) is a challenging task. In this wor...

The aim of this brief was to develop a class of state estimator modified with a projection function to reconstruct the non-measurable variables of a state-constraint system. The main characteristic of this observer was that the estimated states remain inside the compact set defined by the given variables constraints, independently of the output noise and internal modeling uncertainties. The application of the projection operator introduced a non-smooth form for the observer design. Hence, integral Lyapunov functions can be used to realize the stability study. The design of a Lyapunov-Krasovskii functional overcome the smoothness problem and justifies the ultimate boundedness of the estimation error. The upper bound for the estimation error is rationally related to the observer’s lag and it is nonlinear associated with the power of output noises and modeling errors. Two numerical examples (the Chua’s circuit and the ozonation of toxic compounds adsorbed in soil) illustrated the application of the suggested observer.

In this study, a local approximated solution for the Hamilton–Jacobi–Bellman equation based on differential neural networks is proposed. The approximated Value function is used to obtain a feedback control law for a class of uncertain dynamical systems. The approach to deal with the uncertainties of the dynamical system is a min–max method that yields obtaining a robust-like solution for an optimal control problem. The proposed cost functional is presented in the Bolza form and the necessary and sufficient conditions for getting the min–max optimal solution with the designed robust version of the dynamic programming approach are provided. Moreover, the effect of the neural network approximation is studied. All the analysis considers a smoothness assumption regarding the Value function. The practical stability of the system with the neural network feedback optimal control is formally demonstrated by means of the Lyapunov method. Finally, the performance of the control law is compared in simulation with a classical optimal controller. The proposed controller overcomes the results produced by the classical controller, which is confirmed by the functional evaluation.

The design of a state feedback and robust controller for regulating the tridimensional (3D) movement of autonomous underwater mobile crafts (AUMCs). The controller design is based on the applicatio...

The aim of this study was to design a first-order sliding mode controller for dual AC/DC/AC power converters to regulate the production of a corona discharge ozone generator. The design is presented in the two following parts: (a) The first part regulates a three-branch (phase) AC/DC converter to control the DC intermedium voltage that is required to produce the desired ozone concentration, while (b) the second part regulates a one-phase DC/AC power conversion circuit that regulates amplitude of the AC voltage that must be injected into the reaction chamber of the ozone generator. For the first section, the controller regulates the switching sequence yielding the control of the input currents, which defines the amplitude of the DC voltage. In the second, the switching control regulates the amplitude of the expected output AC signal, which depends on the obtained DC voltage from the AC/DC section. This structure represents a novel form to adjust the functioning of the AC/DC/AC power device, which has not been used before in the context of ozone production. Lyapunov’s second method was the main tool for confirming the existence of an asymptotical equilibrium state point for the trajectory tracking deviation for both sections of the power converter. The voltage amplitude was tested on a previously validated mathematical model of a corona-effect ozone generator performance. Several numerical evaluations illustrated the efficient performance of the suggested discontinuous controller and considering the proposed switching sequence that realizes the control action. The proposed controller was contrasted with a usual proportional/integral/derivative (extended state) design, which is a common technique to regulate the ozone generation system.

The main goal of this study is developing an adaptive controller which can solve the trajectory tracking for a class of quadcopter unmanned aerial system (UAS), namely a quadrotor. The control design introduces a new paradigm for adaptive controllers based on the implementation of a set of differential neural networks (DNNs) in the consequence section of a Takagi–Sugeno (T–S) fuzzy inference system. This dynamic fuzzy inference structure was used to approximate the UAS description. The particular form of interaction between neural networks and fuzzy inference systems proposed in the present work received the name of dynamic neural fuzzy system (DNFS). An adaptive controller based on this DNFS form was the main solution attained in this study. This DNFS controller was focused on the estimation and compensation of the uncertain section of the Quadrotor dynamics and then, forced the UAS to perform a hover flight while the tracking of desired angular positions succeeded, which results in tracking a desired trajectory in the X-Y plane. The control design methodology supported on the Lyapunov stability theory guaranteed ultimate boundedness of the estimation and tracking errors simultaneously. Several experimental tests in an outdoor environment by using a real Quadrotor platform was performed by using an RTK-GPS (Real Time Kinematic) system to determine the position of the vehicle in the X-Y plane. The experimental results confirmed the superior performance of the proposed algorithm based on the combination of DNNs and T–S techniques with respect to classical robust controllers.

The aim of this work is to design a robust output-based controller for a robotic manipulator (RM) with a master–slave configuration (MSC). The trajectories of the slave robot manipulator (SRM) must fulfil two types of constraints. The first corresponds to the boundaries of the obstacles placed in the given workspace. The second is related to the boundaries of the workspace. The controller must ensure the collision avoidance of the obstacles and the end-effector of the SRM should remain inside of the workspace. The proposed controller satisfies a state feedback structure with time-varying gains. The time-variable gains include an integral compensation that guarantees the collision avoidance with the obstacle satisfying the boundary of the workspace, which is the main contribution of this study. The solution of a matrix inequality characterises the zone of convergence and the suboptimal control gains. A set of numerical simulations using a MSC based on a couple of two-link RMs illustrates the advantages obtained with the proposed method. Also, a set of experimental results demonstrate the effectiveness of the proposed controller.

This paper proves the ultimately boundedness analysis for the trajectory tracking problem between the states of an uncertain nonlinear system represented by a Takagi–Sugeno (T–S) system and a given...

This manuscript deals with the problem of controlling a virtualized humanoid robot with 16 degrees of freedom (DOF). The aim of this study was to design an output feedback discontinuous controller ...

The aim of this study is to provide a class of state observers, based on differential neural networks, to approximate a class of advanced oxidation systems, based on the application of ozone high oxidant power and catalyst (the named catalytic ozonation). The study considers the design of a state observer for uncertain systems with the restrictions of the ozonation system, including the positivity of the states, as well as the control action. The observer includes a projection operator which is motivated by the state constraints. The learning laws of the proposed differential neural networks are obtained using a class of controlled state restricted Lyapunov functions. The detailed stability analysis proves the input to state stability with respect to the modeling error, as well as the bounded uncertainties of the ozonation system. The experimental confirmation of the state estimation is also presented. The experimental case considers the ozonation of a toxic organic contaminant (therephtalic acid) which is a regular pollutant of the plastic industry wastewater.

International audience; This study is devoted to the design of an adaptive discontinuous control based on differential neural networks (DNNs) for a class of uncertain homogeneous systems. The control is based on the universal approximation properties of artificial neural networks (ANNs) applied on a certain class of homogeneous nonlinear functions. The adaptation laws for the DNNs parameters are obtained with the application of the Lyapunov stability theory and the homogeneity properties of the approximated nonlinear system. The stability analysis of the closed loop system with the proposed controller is presented. The estimation error in the approximation of the uncertain homogeneous functions is considered in the stability analysis. The performance of the controller is illustrated by means of a numerical simulation of a homogeneous model.

A DC voltage source and a DC/DC power converter can be used to control the position, speed, or torque of a DC motor. In such operational conditions, a rectifier is needed to use a DC voltage source if only a three-phase voltage source is available. The objective of this study is to replace a rectifier and DC/DC power converter by one AC/DC power converter, such that its output would be equal to the voltage needed to control a DC motor. It is assumed that the control algorithm of a DC motor is selected, which means that the desired output voltage of the AC/DC converter as a time function or function of the motor state is known. First, a sliding mode methodology is applied to control the converter’s three shoulders to make the three-phase input current track the source voltages multiplied by a time-varying gain. The gain is then selected such that the converter output voltage is equal to the desired input of the DC motor. It is shown that this condition holds if the time-varying gain satisfies a first-order differential equation, which can be implemented as part of the controller. The application of Lyapunov theory confirms that the speed regulation process has a stable equilibrium point at the origin and that the time gain variation is bounded. The power efficiency is equal to one if the gain is positive. A numerical simulation demonstrates application of the developed control methodology for both constant and time-varying angular speed reference inputs.

This article summarizes the comprehensive design of an adaptive control that solves the trajectory tracking of a four-rotor unmanned aerial vehicle supplied by an own-designed grasping device. The controller design uses the regular proportional-derivative (PD) structure which is common to solve regulation, as well as tracking problems for robotic systems. The PD structure needs the estimation of the time-derivative to be exerted on-line. The super-twisting algorithm served to operate as a decentralized estimator of the derivatives for the tracking errors. The controller gains were adjusted by the differential laws aimed to track attainable reference trajectories. The adaptive strategy adjusts the controller gains enforcing the convergence of both the estimation and the tracking errors. A numerical example showed the observer/controller performance. A comparison with a classic non-adaptive PD controller confirms the effectiveness on the tracking task by the proposed design. In addition, a set of virtual numerical evaluations using the parameters of a real quadcopter system confirmed the performance benefits of the adaptive controller based on the PD structure aided with the estimation of the velocity obtained by the observer.

This study aimed to develop a semi non-parametric model of the die casting process of aluminum alloys. This model uses a hierarchical artificial neural network (HANN), with a structure motivated by the relationships of the metals which define the characteristics of the aluminum alloy. These settings depend on the content of seven metals (Sn, Zn, Mn, Cu, Si, Ni, and Mg). The relation between these metals and the alloy characteristics oriented the HANN structure. A distributed back-propagation learning modified with the Levenberg-Marquardt method served to adjust the HANN weights. Two complementary validation methods justified the application of this novel hybrid non-parametric modelling structure. The training set came from standards composition proposed by different international organizations. A set of real aluminum alloys and the experimental results describing their characteristics formed the validation test. An average accuracy value of 3.65% confirmed the ability of the HANN to reproduce the relation between the metal content and the alloy characteristics. These values confirmed how the oriented HANN may predict the aluminum alloy characteristics as function of the metal distribution. This result offers a different alternative to the prediction of aluminum alloy properties using the metal composition as input information.

In this paper, an adaptive disturbance estimation-based control of a class of uncertain feedback linearizable systems with the presence of, both, external perturbations as well as non-modeled dynamics is considered. The aim of the control design was to solve the tracking trajectory problem for a class of output-based linearizable uncertain systems. An adaptive scheme is proposed for developing a state estimator of the uncertain dynamics. The estimation of both, the states and the uncertain dynamics is attained despite the limited knowledge of the plant and the information contained in the output signal. The uncertain section in the linearized system was approximated by a class of time-dependent combination of the system states. The observer implemented a parametric identifier to obtain the time varying parameters associated to the estimation of the uncertain section. This method ensured the adequate estimation process of the uncertainties/perturbations, measured in terms of the mean square error. Simultaneously, an adaptive gain associated to the observer adjusts its trajectories to provide the ultimate boundedness of the estimation error. Once the states of the uncertain system are obtained, a feedback controller rejects actively the perturbations that affect the system by a compensation scheme. Two numerical examples were developed to show the observer-based control performance.

This manuscript introduces a novel methodology to solve the state estimation of discrete-time multi-input multi-output (MIMO) nonlinear systems with uncertain dynamics. The mathematical model of the nonlinear systems considered in this paper satisfies the usual Lagrangian structure that characterizes many mechanical, electrical or electromechanical systems. A recurrent neural network (RNN) estimates the uncertain dynamics of the MIMO system with an updating law based on a particular variant of the discrete-time version of the super-twisting algorithm (DSTA). A Lyapunov stability analysis defines the convergence zone for the state estimation error throughout the solution of a matrix inequality. The convergence zone for the estimation is smaller when the DSTA and the RNN work together in an observer. Numerical examples demonstrate how the adaptive observer reduces the zone of convergence and the oscillations in the steady state compared with a discrete version of the STA with additional linear correcting terms. An experimental implementation shows how the observer estimates the unknown states of a Van Der Pol Oscillator. A comparison against some variations of the DSTA justifies the advantages of the mixed DSTA-RNN observer.

Artificial neural networks (ANNs) are considered efficient tools for modeling complex, non-linear processes with uncertain dynamic models. ANNs were originally applied as effective predictors of diverse processes with static dependence on the input-output information. However, when the ANN must be applied to characterize an approximate model of time-dependent input-output relationships, then it is necessary to introduce the time effect as part of the ANN, yielding to the construction of dynamic ANN or DNN. This review establishes the variants of recurrent and differential forms of DNN, their mathematically formulation as well as the methods to adjust the network weights. The characteristics of DNNs motivate their use to represent the dynamics of decontamination processes. This review details recent findings on the DNN application for the modeling and control of treatment systems based on either biological and chemical processes. The modeling application of DNN for some common methods used in the treatment of wastewater, contaminated soil and atmosphere is described. The major benefits of using the approximate DNN-based model instead of designing the complex mathematical description for each treatment are analyzed in the context of enhancing the efficiency of the decontamination treatment. This review also highlights the remarkable efficiency of DNNs as a keystone tool for modeling and control sequence of treatments. The last section in the review introduces several open researching areas for the application of DNN for decontamination systems based on biochemical and chemical treatments.

In this paper, a non parametric identifier for homogeneous nonlinear systems affine in the input is proposed. The identification algorithm is based on the neural networks using sigmoidal activation functions. The learning algorithm is derived by means of Lyapunov function method and homogeneity theory. A numerical example demonstrates the performance of the proposed identifier.

The aim of this study was to design a step-by-step numerical differentiator for a class of discretized version of a n-th chain-of-integrator system based on the application of the implicit discretization of the super-twisting algorithm (STA). The high-order differentiator reconstructed the non-measurable states of an input-output linearizable systems. The gains of the observer were calculated based on the application of a class of generalized functions. The convergence analysis showed that all the states in the linearized system achieved an invariant set with a predefined size. The existence of this invariant set depends on the uniqueness of the solution for the generalized function. A simple interpretation of a possible exact reconstruction of the non-measurable states of the implicit discretized form. The application of the implicit discretized STA served to design a class of observer for the microalgae culture system.

International audience; The aim of this study is to design a non-parametric identifier for homogeneous systems based on a class of artificial neural networks with continuous dynamics. The identification algorithm is developed for input-affine systems with uncertain gains and diverse degrees of homogeneity. One of the main contributions of this study is the extension of the universal approximation property of neural networks for continuous homogeneous systems. Another contribution is the development of a differential non-parametric identifier based on the novel concept of homogeneous neural networks. The adjustment laws for the weights are obtained from a Lyapunov stability analysis taking homogeneity properties of the system into account. The ultimate boundedness of the origin for the identification error is demonstrated using the persistent excitation condition. The effectiveness of the proposed identifier is verified by the simulation of the three-tank homogeneous model. In this example, the proposed identification scheme is compared with a classical ANN identifier, and we present a statistical analysis of such comparison. It is shown in simulations that the identification error of the proposed homogeneous algorithm has faster convergence and less oscillations.

Unsupervised learning is a target free methodology to classify unorganized information. This study proposes a new unsupervised learning method for classifying unlabeled targets based on convex ellipsoidal sets. The method described here uses ellipsoidal calculus tools to realize pattern classification via a clustering scheme. The algorithm consisted in adjusting the number of clusters defined by an ellipsoidal set as well as their centers, shape forms and orientation. All these processes were realized without preliminary information on the data distribution. The application of an inner gradient descent algorithm permitted the adjustment of these parameters, using the standard deviation of data in the cluster with respect to the semi-axis of ellipsoid that contains the corresponding data. A specific evaluation of the proposed algorithm used two-dimensional attributes databases. The outcomes of the classification results were compared with those produced by the K-means and DBSCAN algorithm. Comparable classification results were achieved overcoming some drawbacks of the methods.

The aim of this study is to design a robust controller for an autonomous underwater vehicle (AUV) based on the application of the extended Integral Sliding Mode (ISM) method. The control problem is reformulated here as an extremum seeking control problem realization for solving the tracking of attainable reference trajectories. The states of the uncertain dynamic corresponding to the AUV dynamics track the references restricted to the x-z plane. The dynamic nature of the AUV induces the application of the ISM extended version design based on the implementation of a sub-gradient strategy to perform the on-line optimization for the tracking error norm. The proposed control permits to minimize the tracking error without a complete knowledge of the AUV dynamics. The trajectory tracking results of the designed controller are compared with the corresponding outcomes enforced by a state feedback and twisting controllers . The proposed controller exhibits better tracking and smaller control magnitude than the state feedback and twisting form. These two results confirm the benefits of introducing the mixed extended strategy, including ISM and dual averaged extremum seeking control.

The aim of this study was to design and evaluate a prototype of a snake-like endoscopic manipulator robot (SLEMR) and its corresponding automatic controller based on the first order sliding mode theory. The SLEMR was controlled with a set of actuators made of shape memory alloys (SMA). The SLEMR device was constructed with a sequential arrangement of links interconnected by a two degree-of-freedom joint. A parallel agonist–antagonist configuration of actuators was implemented to move each joint. The physical relation between temperature and elongation in SMA forced the execution of the movement in the joint. Elongation–temperature model of the SMA actuator served to get a feasible bound of velocity for each joint. Each pair of SMA actuators was controlled by a first order sliding mode controller. This control design solved the tracking trajectory problem for each joint in the SLEMR because of its robustness against uncertainties and external perturbations. The control action was projected into a feasible implementable set of pulse-width modulated signals which was used to regulate the temperature of the corresponding SMA actuator. The controller designed in this study was experimentally validated in a SLEMR made up by a tridimensional printing technique. The control strategy induced the successful trajectory tracking for all the joints in the SLEMR simultaneously. This characteristic of the control design also enforces the tracking of a reference position by the tip of the final link of the SLEMR. An image acquisition system was used to determine the position of the final actuator in the SLEMR. The effectiveness of the controller proposed in this study was confirmed by the evaluation of the tracking error of the final actuator which approached to a bounded region (less than 1.0 mm) near the origin in a finite-time (0.5 s).

This article deals with the control of a class of robotic systems with constant input time delay through the Active Disturbance Rejection paradigm, by means of Generalized Proportional Integral observers. The system is represented as a linear perturbed system, whose lumped disturbance input is estimated and then compensated by an Extended State Observer-Based Control, which is implemented on a predictor scheme for the time delay compensation. A complete Lyapunov Krasovskii functional was used to perform the stability analysis, leading to an ultimate bound trajectory tracking error. The proposal is tested and validated on a two degrees of freedom robotic manipulator.

This study focuses in the output feedback stabilisation of constrained linear systems affected by uncertainties and noisy output measurements. The system states are restricted inside a given polyto...

In this paper, a differential neural network (DNN) implemented as a robust observer estimates the dynamics of perturbed uncertain nonlinear systems affected by exogenous unknown inputs. In the first stage, the identification error converges into a neighborhood around the origin. Then, the second-order sliding mode supertwisting algorithm implemented as a robust exact differentiator reconstructed the unknown inputs. The approach proposed in this paper can be applied in the case of full access to the state vector (identification problem) and in the case of partial access to the state vector (estimation problem). In the second case, the nonlinear system under study must have well-defined full relative degree with respect to the unknown input. Numerical examples showed the effectiveness of the proposed algorithm. The first example tested the DNN working as an identifier into a mathematical model describing the dynamics of a spatial minisatellite. The second example (with a DNN implemented as an observer) tested the methodology of this paper over a single link flexible robot manipulator represented in a canonical (Brunovsky) form. In both examples, the mathematical models served as data generators in the testing of the neural networks. Even when not exact mathematical description of both models was used in the input estimation, the accuracy obtained with the DNN is comparable with the case of applying a high-order differentiator with complete knowledge of the plant.

This study designed a suboptimal output control strategy to characterise an attractive and invariant set for the state trajectories of perturbed linear systems with noisy measurements and state constraints. The state constraints were defined by a given polytope formed of by n-dimensional vectors. An adaptive linear controller enforced the existence of an attractive and invariant set (centred at the origin) for the trajectories of the perturbed system. A barrier Lyapunov function (BLF) and the attractive ellipsoid method (AEM) derived the adjustment law of the adaptive gain. The controller design used the linear matrix inequality technique to solve two optimisation problems. The first solution provided a maximal set where the initial conditions must belong without violating the state constraints. The second optimisation solution characterised the invariant minimal attractive set for the system trajectories. An academic example verified how the proposed adaptive control generated the system trajectories that converged to the minimal attractive ellipsoid while keeping them inside the polytope defining the state constraints. The simulation script showed the advantages of the adaptive BLF controller (ABLC) against classical AEM controller. A second numerical example considered a direct current motor showing the advantages of the ABLC against the sliding mode technique.

The aim of this study was to develop a prototype of an orthotic system that can be used as a support tool in the rehabilitation of the upper limb. The construction of this device was motivated by the increasing number of subjects suffering from full or partial loss of the upper limb function as a consequence of spinal cord injuries, strokes, occupational syndromes and sports injuries. The majority of procedures used in upper limb rehabilitation consist of repetitive movements enforced by physiotherapists; a robotic device executing the same tasks seems to be a plausible solution if the orthosis can be programmed and controlled automatically. This study reports the mechanical design, electronic instrumentation and automatic control of an upper limb orthosis made of plastic polymer that makes the orthosis a wearable and self-carrying device. The orthosis consisted of a mechatronic device with five joints. The pieces made by a three-dimensional plastic printer were used to construct the device leading to a total weight of 2.6 kg. The application of a robust automatic controller based on the sliding-mode theory forces the movement of the arm, while taking into account the constraints in each angular displacement of the orthosis. A set of reference trajectories designed to represent the usual movements of a healthy upper limb served for evaluating the controller execution. The orthosis was tested on 15 volunteers with a maximum experimental steady-state error of 2% in the angular deviation of all articulations with respect to their reference trajectories.

This study deals with the design of an automatic controller to solve the problem of trajectory tracking for collaborative robot manipulators. The control algorithm corresponds to an adaptive proportional derivative controller (APDC) aimed to reduce the needed energy to execute the tracking of some predefined reference trajectories. The controller was designed with the aim of keeping a constant distance between the final effectors of both manipulators. The derivative estimation used in the APDC was obtained by a set of robust exact differentiators based on the application of the super-twisting algorithm (STA). The controller was tested on two real cooperative multi-articulated robotic manipulators system. The experimental setup consisted of two robot manipulators designed with four degrees of freedom each one constructed by the 3D printing technology. The experimental results included comparisons with respect to the classical non-adaptive proportional-derivative controllers. The superior performance of the adaptive controller proposed in this study was confirmed by the estimation of the least mean square analysis of the tracking error.

The aim of this study was to design a discontinuous controller with adaptive gains, based on the sliding-mode theory. The adaptive controller solved the trajectory tracking problem for a class of systems with state constraints, specifically for a class of multi-articulated robot manipulator with a constraint work-space. The controller implemented a state dependent adaptive gain that grows in value when the trajectories approach the boundary of the set that characterized the states constraints. The design of the adaptive gain guaranteed the existence of a finite-time stable equilibrium point for a special sliding surface depending on the tracking trajectory error. The specific law used to adjust the gain was obtained by a Lyapunov-based stability analysis. Some numerical simulations proved that the sliding-mode controller showed a superior performance, measured by the mean square value of the tracking result, compared to the non-adaptive gain first order sliding-mode controller.

This paper presents the development of a hybrid model that describes the temperature, elongation and inner force relationships in a spring Shape Memory Alloy (SMA) actuator. The temperature-inner force relationship obeys a hybrid structure in which a sigmoid function correlates the variation of temperature for the SMA and the force executed by the spring actuator. The hybrid nature of the model describes the regular hysteresis behavior of the SMA. The switching law of the hybrid model depends on the time derivative of the temperature. A multivariable model depending on temperature, and inner and external forces was developed in order to characterize the Shape Memory Effect (SME). A set of experiments was carried out to obtain the parameters used to characterize the model. The application of the Levenberg-Marquardt method resulted in the parametric estimation procedure. An averaged correlation factor of 0.95 between the model response and experimental results justifies the proposed modeling approach.

This study solves a finite horizon optimal problem for linear systems with parametric uncertainties and bounded perturbations. The control solution considers the uncertain part of the system in the sub-optimal control solution by proposing a min-max problem solved by a dynamic neural programming approximate solution. The structure of the neural network was proposed to satisfy the charcateristics of the value function including possitiveness and continuity. The impact of the presence of bounded perturbation over the Hamiltonian maximization was analyzed in detail. The explicit learning law used to adjust the weights was obtained directly from the Hamilton-Jacobi-Bellman (HJB) approximate solution. The weights adjustment to the proposed algorithm is based on an on-line state dependent Riccati-like equation. A numerical simulation is presented to illustrate the results of the sub-optimal algorithm including its comparison against the classical linear regulator solved considering the non-perturbed system.

The identification problem incorporated in feedback control of uncertain nonlinear systems exhibiting complex behavior has been solved in different ways. Some of these solutions have used artificial intelligence methods like fuzzy logic and neural networks. However, their individual implementation suffers from certain drawbacks, such as the black-box nature of neural network and the problem of finding suitable membership functions for fuzzy systems. These weaknesses can be avoided by implementing a hybrid structure combining these two approaches, the so-called neuro-fuzzy system. In this paper, a neuro-fuzzy system that implements differential neural networks (DNNs) as consequences of Takagi–Sugeno (T–S) fuzzy inference rules is proposed. The DNNs substitute the local linear systems that are used in the common T–S method. In this paper, DNNs are used to provide an effective instrument for dealing with the identification of the uncertain nonlinear system, while the T–S rules are used to provide the framework of previous knowledge of the system. The main idea is to carry out an online identification process of an uncertain nonlinear system with the aim to design a closed-loop trajectory tracking controller. The methodology developed in this study that supports the identification and trajectory control designs is based on the Lyapunov formalism. The DNN implementation results in a time-varying T–S system. As a consequence, the solution of two time-varying Riccati equations was used to adjust the learning laws in the DNN as well as to adjust the gains of the controller. Two results were provided to justify the existence of positive-definite solutions for the class of Riccati equations used in the learning laws of DNNs. A complete description of the learning laws used for the set of DNN identifiers is also obtained. An autonomous underwater vehicle system is used to demonstrate the performance of the controller on tracking a desired 3-D path by this combination of the DNN and the T–S system.

In the developed world, heart diseases are the major cause of death among adults. Often, the sufferers of heart disease are not aware of their condition until a catastrophic medical event occurs. Therefore, early online detection and continuous monitoring of abnormal heart rhythms shall reduce this occurrence. There are four main types of arrhythmia: ventricular arrhythmia, supraventricular arrhythmia, premature beats and asynchronous arrhythmia. In this study, an algorithm for automatic detection of atrial premature contraction, supraventricular tachyarrhythmias, fusion of ventricular and normal beat (FUSION), isolated QRS-like artifact (ARFCT), ST change, T-wave change, premature or ectopic supraventricular beat and normal beat (NORMAL) using a continuous neural network (CoNN) is presented. This kind of continuous classifier offers an online detection of classical arrhythmia observed in electrocardiographic (EKG) signals. Typically, due to its complexity and recursive nature of arrhythmia classification algorithms, they are difficult to be implemented in real time. In this work, automatic signal classification was attained by implementing a parallel CoNN algorithm using fixed point arithmetic on a field-programmable gate array (FPGA). First, the classification algorithm using a floating-point MATLAB implementation was developed and validated. This procedure served as a benchmark for the fixed point FPGA implementation on a Xilinx Zinq board. The performance of the classification algorithm was evaluated by using a fivefold cross-validation method, achieving a 93.80% accuracy and a sensitivity (TPR) average of 98% when performing the classification of the entire set of EKG signal samples.

This paper addresses the design of a normalized convergent learning law for neural networks (NNs) with continuous dynamics. The NN is used here to obtain a nonparametric model for uncertain systems described by a set of ordinary differential equations. The source of uncertainties is the presence of some external perturbations and poor knowledge of the nonlinear function describing the system dynamics. A new adaptive algorithm based on normalized algorithms was used to adjust the weights of the NN. The adaptive algorithm was derived by means of a nonstandard logarithmic Lyapunov function (LLF). Two identifiers were designed using two variations of LLFs leading to a normalized learning law for the first identifier and a variable gain normalized learning law. In the case of the second identifier, the inclusion of normalized learning laws yields to reduce the size of the convergence region obtained as solution of the practical stability analysis. On the other hand, the velocity of convergence for the learning laws depends on the norm of errors in inverse form. This fact avoids the peaking transient behavior in the time evolution of weights that accelerates the convergence of identification error. A numerical example demonstrates the improvements achieved by the algorithm introduced in this paper compared with classical schemes with no-normalized continuous learning methods. A comparison of the identification performance achieved by the no-normalized identifier and the ones developed in this paper shows the benefits of the learning law proposed in this paper.

This paper presents the design and implementation of an output feedback controller based on the super twisting algorithm (STA) that stabilizes the trajectory tracking error of a skid steered mobile robot (SSMR). The control scheme introduces a diffeomorphism based on the mathematical model of the SSMR to transform the original problem into a third order chain of integrators. In this study, the available measurements are the position and orientation of the SSMR. A modified STA working as a step by step differentiator estimates the velocity and acceleration of the mobile robot. Then, a second STA enforces the tracking of a predefined trajectory. Numerical and experimental results comparing the STA with a state feedback controller (SFC) and a first order sliding mode controller (FOSM) justify the control proposal.

In recent years, hundreds of technical papers have been published which describe the use of sliding mode control (SMC) techniques for power electronic equipment and electrical drives. SMC with discontinuous control actions has the potential to circumvent parameter variation effects with low implementation complexity. The problem of controlling time-varying DC loads has been studied in literature if three-phase input voltage sources are available. The conventional approach implies the design of a three-phase AC/DC converter with a constant output voltage. Then, an additional DC/DC converter is utilized as an additional stage in the output of the converter to generate the required voltage for the load. A controllable AC/DC converter is always used to have a high quality of the consumed power. The aim of this study is to design a controlled continuous signal generator based on the sliding mode control of a three-phase AC-DC power converter, which yields the production of continuous variations of the output DC voltage. A sliding mode current tracking system is designed with reference phase currents proportional to the source voltage. The proportionality time-varying gain is selected such that the output voltage is equal to the desired time function. The proposed new topology also offers the capability to get rid of the additional DC/DC power converter and produces the desired time-varying control function in the output of AC/DC power converter. The effectiveness of the proposed control design is demonstrated through a wide range of MATLAB/Simulink simulations.

The design of an artificial neural network (ANN) based sub-optimal controller to solve the finite-horizon optimization problem for a class of systems with uncertainties is the main outcome of this study. The optimization problem considers a convex performance index in the Bolza form. The dynamic uncertain restriction is considered as a linear system affected by modeling uncertainties, as well as by external bounded perturbations. The proposed controller implements a min–max approach based on the dynamic neural programming approximate solution. An ANN approximates the Value function to get the estimate of the Hamilton–Jacobi–Bellman (HJB) equation solution. The explicit adaptive law for the weights in the ANN is obtained from the approximation of the HJB solution. The stability analysis based on the Lyapunov theory yields to confirm that the approximate Value function serves as a Lyapunov function candidate and to conclude the practical stability of the equilibrium point. A simulation example illustrates the characteristics of the sub-optimal controller. The comparison of the performance indexes obtained with the application of different controllers evaluates the effect of perturbations and the sub-optimal solution.

This manuscript deals with the problem of controlling a virtualized humanoid robot with 16 degrees of freedom (DOF), each corresponding to the articulation in a real human being. That is, three DOF for each leg in the sagittal plane and one for the abduction movement; three DOF for each arm in the sagittal plane and one for the waist. The tracking trajectory problem of any humanoid robot like the classical biped robots requires a control algorithm with robustness against parametric uncertainties, fast response and even with finite-time convergence. These main characteristics are easily covered by sliding mode controllers. This manuscript implements a terminal second order sliding mode (TSOSM) controller to ensure the finite-time tracking trajectory of each articulation of the humanoid robot to the ones that define a classical walking pattern obtained by bio-mechanical studies. The TSOSM is implemented in a virtual platform developed in a computer-aided design software.

The objective of this study was to design of an output based impedance adaptive controller for a special class of cervical orthoses, a class of biomedical devices for the rehabilitation of neck illnesses. The controller used the adaptive sliding mode theory to enforce the tracking of the reference trajectory if the patient was not resistant to the therapy. If the patient rejects the orthosis activity, a second impedance-based controller governs the orthosis movement allowing the patient to take the leading role in the orthosis sequence of movements. The proposed controller considers a weighted controller combining the tracking and the impedance controls in a single structure. The monitoring of the external force was evaluated on a novel weighting function defining on-line the role of each controller. The proposed orthosis was motivated by the prevalence of whiplash, which is a syndrome that is produced by forced hyperextension and hyperflexion of the neck. This study included the development of a technological prototype of the orthotic type to support the recovery of patients diagnosed with whiplash. The sections that make up the orthotic device are two independent systems that move the patient’s head in the sagittal and frontal planes. For this purpose, the mechanical structure of the cervical orthosis was made up of 7 pieces printed in 3D with polylactic acid (PLA). The operation of the cervical orthosis was evaluated in two sections: (a) using a simulation system, which consists of a spring with an artificial head and the development of a graphic interface in Matlab, and (b) evaluating the controller on the proposed orthosis. With these elements, the follow-up of the trajectory proposed by the actuators was evaluated, as well as its performance in the face of the opposition that a patient generates. The superiority of the proposed controller was confirmed by comparing the tracking efficiency with proportional-integral-derivative and first-order sliding variants.

A new method to design learning laws for neural networks with continuous dynamics is proposed in this study. The learning method is based on the so-called double-averaged descendant technique (DASGDT), which is a variant of the gradient-descendant method. The learning law implements a double averaged algorithm which filters the effect of uncertainties of the states, which are continuously measurable. The learning law overcomes the classical assumption on the strict convexity of the functional with respect to the weights. The photocatalytic ozonation process of a single contaminant is estimated using the learning law design proposed in this study.

This study presents the design of a state feedback controller for an Unmanned Underwater Mobile Vehicle (UUMV) considering the implementation of an Averaged Sub-Gradient (ASG) version of the Integral Sliding Modes (ISM) method. The control problem is formulated here as an extreme seeking problem for the UUMV dynamics, which must track attainable reference trajectories in three-dimensional space. The dynamic nature of the UUMV induces the application of the extended version of ISM, where the integral term represents an ASG of the tracking error norm. The realized trajectory tracking is compared with the trajectories enforced by a traditional state feedback controller with gravity effect compensation. The proposed controller exhibits better tracking and similar control magnitude than the considered classical state feedback realization. These two results confirm the benefits of introducing the mixed extended strategy, including ISM and ASG as an extreme seeking controller for the considered UUMV.

The aim of this work was to design a non-parametric model of interconnected systems represented by uncertain second-order systems with incomplete information (only the generalized position vector is measurable). Artificial neural networks appeared to be a plausible alternative to get a non-parametric representation of the aforementioned interconnected systems. The modelling strategy used a set of spatial distributed second-order continuous neural networks (CNN). Each node in the interconnected system was represented as a second-order continuous neural network added by the super-twisting discontinuous sliding mode algorithm. The non-parametric modelling problem was reduced to design a feasible expression for the CNN weights in order to reproduce the states (including the generalized derivative of position vector) of all the nodes dynamics together and simultaneously. The adaptive laws for the CNN weights ensured the convergence of the CNN trajectories to the states of the uncertain interconnected s...

Most of the research in sliding mode theory has been carried out to in continuous time to solve the estimation and control problems. However, in discrete time, the results in high order sliding modes have been less developed. In this paper, a discrete time super-twisting-like algorithm (DSTA) was proposed to solve the problems of control and state estimation. The stability proof was developed in terms of the discrete time Lyapunov approach and the linear matrix inequalities theory. The system trajectories were ultimately bounded inside a small region dependent on the sampling period. Simulation results tested the DSTA. The DSTA was applied as a controller for a Furuta pendulum and for a DC motor supplied by a DSTA signal differentiator. (C) 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Graphical abstractDisplay Omitted HighlightsWe proposed a method to solve the identification of uncertain distributed parameter systems.We developed a novel DNN structure based on the finite element method.We derived adaptive learning laws using Lyapunov's second method.The identification algorithm is developed in Nvidia's CUDA/C to reduce the execution time.The FEM-DNN algorithm that we present was compared with a neural network trained using group search optimization or GPO-NN, and showed a superior performance.The algorithm was validated with a 3D simulated DPS and tested on a physical 2D experiment. Most of the previous work on identification involves systems described by ordinary differential equations (ODEs). Many industrial processes and physical phenomena, however, should be modeled using partial differential equations (PDEs) which offer both spatial and temporal distributions that are simply not available with ODE models. Systems described by a PDE belong to a class of system called distributed parameter system (DPS). This article presents a method for solving the problem of identification of uncertain DPSs using a differential neural network (DNN). The DPS, assumed to be described by a PDE, is approximated using the finite element method (FEM). The FEM discretizes the domain into a set of distributed and connected nodes, thereby, allowing a representation of the DPS in a finite number of ODEs. The proposed DNN follows the same interconnection structure of the FEM, thus allowing the DNN to identify the FEM approximation of the DPS in both 2D and 3D domains. Lyapunov's second method was used to derive adaptive learning laws for the proposed DNN structure. The identification algorithm, here developed in Nvidia's CUDA/C to reduce the execution time, runs mostly on the graphics processing unit (GPU). A physical experiment served to validate the 2D case. In the experiment, the DNN followed the trajectory of 57 markers that were placed on an undulating square piece of silk. The proposed DNN is compared against a method based on principal component analysis and an artificial neural network trained with group search optimization. In addition to the 2D case, a simulation validated the 3D case, where input data for the DNN was generated by solving a PDE with appropriate initial and boundary conditions over an unitary domain. Results show that the proposed FEM-based DNN approximates the dynamic behavior of both a real 2D and a simulated 3D system.

This study addressed the problem of robust control of a biped robot based on disturbance estimation. Active disturbance rejection control was the paradigm used for controlling the biped robot by direct active estimation. A robust controller was developed to implement disturbance cancelation based on a linear extended state observer of high gain class. A robust high-gain scheme was proposed for developing a state estimator of the biped robot despite poor knowledge of the plant and the presence of uncertainties. The estimated states provided by the state estimator were used to implement a feedback controller that was effective in actively rejecting the perturbations as well as forcing the trajectory tracking error to within a small vicinity of the origin. The theoretical convergence of the tracking error was proven using the Lyapunov theory. The controller was implemented by numerical simulations that showed the convergence of the tracking error. A comparison with a high-order sliding-mode-observer-based controller confirmed the superior performance of the controller using the robust observer introduced in this study. Finally, the proposed controller was implemented on an actual biped robot using an embedded hardware-in-the-loop strategy.

The aim of this study was to design an adaptive control strategy based on recurrent neural networks RNNs. This neural network was designed to obtain a non-parametric approximation identification of discrete-time uncertain nonlinear systems. A discrete-time Lyapunov candidate function was proposed to prove the convergence of the identification error. The adaptation laws to adjust the free parameters in the RNN were obtained in the same stability analysis. The control scheme used the states of the identifier, and it was developed fulfilling the necessary conditions to establish a behavior comparable with a quasi-sliding mode regime. This controller does not use the regular form of the switching function that commonly appears in the sliding mode control designs. The Lyapunov candidate function to design the controller and the identifier simultaneously requires the existence of positive definite solutions of two different matrix inequalities. As consequence, a class of separation principle was proven when the RNN-based identifier and the controller were designed by the same analysis. Simulations results were designed to show the behavior of the proposed controller solving the tracking problem for the trajectories of a direct current DC motor. The performance of the proposed controller was compared with the solution obtained when a classical proportional derivative controller and an adaptive first-order sliding mode controller assuming poor knowledge of the plant. In both cases, the proposed controller showed superior performance when the relation between the tracking error convergence and the energy used to reach it was evaluated. Copyright © 2016 John Wiley & Sons, Ltd.

A robust control feedback strategy is developed to solve the stabilization problem of constrained systems with uncertainties and output perturbations. The states are assumed to be constrained inside a given polytope and the perturbations bounded. The control law is developed using an extended version of the attractive ellipsoid method (AEM) approach, and a barrier Lyapunov function (BLF); this is a function whose value goes to infinity whenever its arguments approach to the boundary of a given set. The control parameters are obtained through the solution of some optimization problems related to the approximation of the constraints set and the characterization of a minimal ultimate bounded set for the system trajectories. The implementability of the resulting algorithm is supported by a numerical example and by the comparison with the regular AEM based on a quadratic Lyapunov function.