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This study presents the development of an event-driven hybrid control for position and force tracking applied on a mobile robotic manipulator for metal recycling tasks. The suggested controller operates in a sequenced strategy starting from a fixed spot, moving the mobile device towards a targeted zone ($\Omega _i^r$ Ω i r ) from where the i-th piece-to-be-recycled is attainable (considering the arm manipulation). Once the event of entering the zone is completed, the mobile robot is fixed at a position, and the end-effector of the robotic arm is enforced towards the piece-to-be-recycled. When the end-effector touches the piece in a given spot ($\Omega _i^e$ Ω i e ), the hybrid control changes to the force tracking intending to carry the piece towards the spot ($\Omega _i^p$ Ω i p ) where it ill be processed. Each piece location is identified based on a vision-based system that applies deep learning tools using convolutional neural networks. A multi-physics numerical simulation illustrated the application of the developed controller in a realistic scenario, showing all the elements of the event-driven operation. To validate the suggested controller, the comparison with a robust control that works on a wide range of carrying mass confirms the operational improvement of the event-driven hybrid position and force design. [ABSTRACT FROM AUTHOR]

This research focuses on designing a min–max robust control based on a neural dynamic programming approach using a class of continuous differential neural networks (DNNs). The proposed controller solves the robust optimization of a proposed cost function that depends on the trajectories of a system with an uncertain mathematical model satisfying a class of non-linear perturbed systems. The dynamic programming min–max formulation enables robust control concerning bounded modelling uncertainties and disturbances. The Hamilton–Jacobi–Bellman (HJB) equation's value function, approximated by a DNN, permits to estimate the closed-loop formulation of the controller. The controller design is based on an estimated state trajectory with the worst possible uncertainties/perturbations that provide the degree of robustness using the proposed controller. The class of learning laws for the time-varying weights in the DNN is produced by studying the HJB partial differential equation. The controller uses the solution of the obtained learning laws and a time-varying Riccati equation. A recurrent algorithm based on the Kiefer–Wolfowitz method leads to adjusting the initial conditions for the weights to satisfy the final condition of the given cost function. The robust control suggested in this work is evaluated using a numerical example confirming the optimizing solution based on the DNN approximate for Bellman's value function. [ABSTRACT FROM AUTHOR]

This study presents the design of a robust control based on the sliding-mode theory to solve both; the stabilization and the trajectory tracking problems of nonlinear systems subjected to a class of full-state restrictions. The selected nonlinear system satisfies a standard Lagrangian structure affected by nonparametric uncertainties. A barrier Lyapunov function is used to ensure the state constraints by designing a time-varying gain, which guarantees the fulfillment of the predefined state constraints even under external perturbations. The proposed design methodology for the barrier sliding-mode control (BSMC) ensures the convergence of the sliding surface in finite time to the origin. Consequently, the asymptotic convergence of the states to the corresponding equilibrium point is achieved. The finite-time stability of the origin in the closed-loop system with the proposed controller has been demonstrated using the second Lyapunov stability method. The suggested controller was evaluated on a two-link robotic manipulator. Then, the obtained results showed better stabilization and tracking performances (while the restrictions are satisfied) than the traditional first-order sliding-mode or linear state feedback controllers. [ABSTRACT FROM AUTHOR]

The aim of this study is to develop an adaptive automatic control method for solving the trajectory tracking problem for a biped robotic device (BRD) and taking into account that each articulation is mobilized by a linear actuator. Each extremity of the BRD has three articulations with a linear actuator enforcing the controlled motion for each articulation. The control problem considers the task of tracking reference trajectories that define a regular gait cycle. The suggested adaptive control form has state-dependent gains that drive the tracking error into an invariant and attractive ellipsoidal with a center at the origin; meanwhile, the articulation restrictions are satisfied permanently. The stability analysis based on a controlled Lyapunov function depending on the tracking error leads to the explicit design of the state-dependent adaptive gains. Taking into account the forward complete setting of the proposed BRD, an output feedback formulation of the given adaptive controller is also developed using a finite-time and robust convergent differentiator based on the super-twisting algorithm. A virtual dynamic representation of the BRD is used to test the proposed controller using a distributed implementation of the adaptive controller. Numerical simulations corroborate the convergence of the tracking error, while all the articulation restrictions are satisfied using the adaptive gains. With the purpose of characterizing the proposed controller, a sub-optimal tuned regular state feedback controller is used as a comparative approach for validating the suggested design. Among the compared controllers, the analysis of the convergence of the mean square error of the tracking error motivates the application of the designed adaptive variant. [ABSTRACT FROM AUTHOR]

This study has the aim of introducing a new type of trajectory tracking robust controllers for a class of rehabilitation robotic system considering the articulations restrictions. The robotic device consists of a suspended biped configuration. The suggested robust control considers the application of state depending gains which provide finite-time convergence for the tracking deviation. The state restrictions are fulfilled by the implementation of controller gains estimated by a class of the controlled tangent barrier Lyapunov function. Stability analysis for the tracking error yields the explicit design of the state dependent gains. The rate of convergence for the controller design is enhanced using a matrix inequality convex optimization method. Based on the forward complete characteristic of the suggested rehabilitation device, it is allowed using a finite-time convergent super-twisting-based differentiator to concrete an output feedback realization of the proposed controller. A computerized model of the tendered rehabilitation robot provides a reliable testing platform to the suggested roust controller. Numerical evaluations appear to serve as an indirect confirmation for the tracking error convergence, satisfying the articulation restrictions, and the effect of the gain optimization design. For comparison purposes, the regular state feedback control design is considered as benchmark. The faster convergence of the mean square estimation of the tracking error justifies the design of the proposed control design as well as the state feedback structure justifies the origin is a fixed-time stable equilibrium point for the space of tracking error at the same time that state space restrictions remain satisfied. The experimental evaluations of the proposed controller justifies the barrier controller which, in spite of the modeling uncertainties and the implementation issues, tracked the reference trajectories. [ABSTRACT FROM AUTHOR]

The current study presents an adaptive control approach to solve the tracking trajectory problem for a robotic manipulator that uses a gripper based on bimorph piezoelectric actuators. The development of an adaptive gain state feedback form that considers the state restrictions is proposed using a novel class of barrier Lyapunov function that drives the effective control of joints and piezoelectric actuators. The proposed method allows for the inclusion of complex combinations of state restrictions in the Lyapunov function, yielding the construction of differential forms for the gains in the controller that can handle the evolution of trajectories of the robotic arm inside the restricted region. The proposed control design successfully tracks reference trajectories for both joints of the robotic arm as well as the motion of the piezoelectric device during several operative scenarios. A comprehensive experimental study evaluates the effect of introducing state-dependent gain considering state restrictions of the ellipsoidal type. The comparison of the mean square error confirms the contributions of the developed control action, showing better tracking quality for less control power with the same evaluation, which is a desirable characteristic in the controlled motion of micromanipulators. The proposed controller solves the tracking trajectory problem for the micromanipulation system, satisfies the motion restrictions, and allows better tracking performance to be enforced. Furthermore, comparison of the obtained trajectories seems to validate the proposed controller's contribution concerning a feedback form with fixed gains. [ABSTRACT FROM AUTHOR]

This study focuses on developing a continuous differential neural network (DNN) approximating min–max robust control by applying dynamic neural programming. The suggested controller is applied to a class of nonlinear perturbed systems providing satisfactory dynamics for a given cost function depending on both the trajectories of the perturbed system and the designed constrained control actions. The min–max formulation for dynamic programming offers reliable control for restricted modeling uncertainties and perturbations. The suggested design considers control norm restrictions in the optimization problem. DNN's approximation of the worst (with respect to the admissible class of perturbations and uncertainties) value function of the Hamilton–Jacobi–Bellman (HJB) equation enables the estimation of the closed-loop formulation of the controller. The robust version of the HJB partial differential equation is studied to create the learning law class for the time-varying weights in the DNN. The controller employs a time-varying Lyapunov-like differential equation and the solution of the corresponding learning laws. A recurrent algorithm based on the Kiefer–Wolfowitz technique can be used by modifying the weights' initial conditions to fulfill the specified cost function's end requirements. A numerical example tests the robust control proposed in this study, validating the robust optimal solution based on the DNN approximation for Bellman's value function. • A robust optimal control is developed using approximate neural dynamic programming. • Robust optimal control is solved for nonlinear systems with restricted control actions. • A differential neural network is used to approximate Belman's function for Hamilton–Jacobi–Bellman equation. • The learning laws are derived based on the Hamilton–Jacobi–Bellman equation. [ABSTRACT FROM AUTHOR]

The design of an output-based robust disturbance rejection controller, aimed to solve the state tracking for the articulations of an experimental biped robot, was the main outcome of this study. The robust disturbance rejection controller included an auxiliary hybrid observer entailed to recover the angular velocity for each articulation. The estimated states served to perform the approximation of disturbances and non-modeled parts in the biped robot dynamics by implementing an extended state observer structure. The observer used the tracking position errors as input information, as well as considering the limb articular constraints, which are natural for biologically inspired biped robots. The effect of state constraints motivated the implementation of a hybrid observer with saturated output error injection. The controller design used the estimation of constraint velocity for solving the design of a tracking trajectory control to resolve the reproduction of the gait cycle by the bipedal robotic system. The Lyapunov stability theory served to obtain the laws which adjust the observer gains as well as to prove the ultimate boundedness of the tracking error as well. The evaluation of the suggested controller was realized on a numerical representation of the biped robot. These simulations illustrated the tracking performance of the hybrid robust disturbance rejection controller for all biped robot articulations in a decentralized structure. Experimental evaluations were also considered to validate the robust disturbance rejection controller design. A fully actuated biped robot was constructed and controlled by the robust disturbance rejection controller. The tracking results obtained by the robust disturbance rejection controller (in both the numerical and experimental evaluations) overcame the classical approach performances of diverse controllers as state feedback (proportional-derivative form) and regular robust disturbance rejection controller which did not consider the articulation constraints. [ABSTRACT FROM AUTHOR]

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 application of Averaged Sub-Gradient Integral Sliding Mode Realisation (ASGISMR). The application of the ASGISMR yields the solution of the closed-loop extreme seeking control for a non-strictly convex functional depending on the tracking error between reference and 3D position of the AUMC. The design of reference trajectories was proposed to enforce the AUMC to follow a continued submersion and ellipsoidal detouring. The mechanical dynamical form of AUMC is well posed for applying the extended version of ASGISMR, considering that integral term represents an ASG associated to the euclidean norm of the tracking error. The time evolution of the functional over the controlled trajectories of the AUMC is compared with the corresponding functional enforced by a traditional state feedback controller with gravity effect compensation. The proposed controller exhibits better tracking and similar control magnitude than the considered reference state feedback realisation. These outcomes justify the potential contributions of the suggested ASGISMR to obtain the local minimisation of the evaluated functional, considering such controller as an extreme seeking realisation for the proposed AUMC. [ABSTRACT FROM AUTHOR]

The aim of this study was to design a constrained robust output feedback control strategy for stabilizing linear systems affected by uncertainties and output perturbations. The input is constrained by a saturation function. A classical Luenberger observer reconstructed the states from output observations. The state feedback control employed the estimated states given by the observer. This work proposed a Barrier Lyapunov Function (BLF) to manage the saturation problem in the control input. Moreover, an extended version of the attractive ellipsoid method (AEM) characterized the zone of convergence due the presence of perturbations in the output. A convex optimization procedure, formulated as a set of matrix inequalities, yielded the control parameters and the region of attraction for the close‐loop system as well as a minimal ultimately bounded set for the system trajectories. Numerical simulations supported the theoretical results formulated in this study. [ABSTRACT FROM AUTHOR]

Summary: This study aims to design a robust state feedback controller for uncertain and perturbed linear systems with state constraints described by a polytope. This novel design incorporates the use of a composite barrier Lyapunov function (CBLF) and the convex hull of a set of ellipsoids inscribed in the given polytopic constraint set. The CBLF is used to ensure that this convex hull is an invariant set for the perturbed system states. Then, an optimization scheme is implemented to maximize the size of this invariant set to use it as a safe set. This is a set of initial conditions ensuring that the system solutions conform to the constraints for any subsequent time instant. Additionally, a minimal ultimate bound for the states is calculated to ensure asymptotic convergence to a region as close to the origin as possible. This region is characterized by a second convex hull of ellipsoids using the well‐known attractive ellipsoid method and the CBLF. Numerical simulations illustrate and compare the obtained results against a similar approach, considering the classical quadratic Lyapunov function, instead of the CBLF. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 polytope and a classical Luenberger observer is used to reconstruct the unmeasurable states from output observations. Based on the observed states, a state feedback is proposed as the control input. The stability analysis and the control design are done using an extended version of the attractive ellipsoid method (AEM) approach. To avoid the violation of state constraints, this work proposes a barrier Lyapunov function (BLF) based analysis. The control parameters are obtained throughout the solution of some optimisation problems such that the BLF ensures an approximation of the constraints by a maximal ellipsoidal set and the AEM provides the characterisation of a minimal ultimately bounded set for the closed-loop system solutions. Numerical simulations show the advantages using the BFL-AEM methodology against classical sub-optimal controllers in academic second order and third order examples. Then, the proposed control strategy is applied over a Buck DC-DC converter. In all the cases, the method proposed here prevails over the other controllers. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The problem of robust control applied to adjust the configuration of an ankle prosthesis based on disturbance estimation has been addressed in this study. Active disturbance rejection control was the paradigm used for controlling the robotic prosthesis by means of a direct active estimation. Based on this active estimation, the robust controller implemented the disturbance cancellation providing a fast converge to the origin of the tracking error. The uncertainties affecting the prosthesis dynamics were identified by a high‐order extended state high gain observer. This identification was used to force the tracking between the actual position and force needed in the ankle prosthesis and some reference values obtained by a biomechanical gait cycle analysis. Therefore, the estimated states were used to implement a robust output feedback controller that was effective to reject actively the perturbations. This rejection implemented within the controller forced the trajectory tracking to a small vicinity of the origin. A strategy based on composite Lyapunov function served to prove that tracking problem for the prosthesis was successfully solved despite the switching nature of the gait cycle. The controller was implemented in numerical simulations for showing the convergence of the tracking error. The convergence of this tracking error to the region around the origin was obtained within the first second of simulation. [ABSTRACT FROM AUTHOR]

This research is dedicated to developing a min–max robust control strategy for a dynamic game involving pursuers, evaders, and defenders in a multiple-missile scenario. The approach employs neural dynamic programming, utilizing multiple continuous differential neural networks (DNNs). The competitive controller devised addresses the robust optimization of a joint cost function that relies on the trajectories of the pursuer–evader–defender system, accommodating an uncertain mathematical model while adhering to control restrictions. The dynamic programming min–max formulation facilitates robust control by accounting for bounded modeling uncertainties and external disturbances for each game component. The value function of the Hamilton–Jacobi–Bellman (HJB) equation is approximated by a DNN, enabling the estimation of the closed-loop formulation for the joint dynamic game with state restrictions. The controller’s design is grounded in estimating the state trajectory under the worst possible uncertainties and perturbations, providing a robustness factor through the robust neural controller. The learning law class for the time-varying weights in the DNN is generated by studying the HJB partial differential equation for the missile motion for each player in the dynamic game. The controller incorporates the solution of the obtained learning laws and a time-varying Riccati equation, offering an online solution to the control implementation. A recurrent algorithm, based on the Kiefer–Wolfowitz method, adjusts the initial conditions for the weights to satisfy the final condition of the given cost function for the dynamic game. A numerical example is presented to validate the proposed robust control methodology, confirming the optimization solution based on the DNN approximation for Bellman’s value function. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The properties of robustness and finite‐time convergence provided by sliding mode (SM) theory have motivated several researches to deal with the problems of control and state estimation. In the SM theory, the super‐twisting algorithm (STA), a second‐order SM scheme, has demonstrated remarkable characteristics when it is implemented as a controller, observer or robust signal differentiator although the presence of noise and parametric uncertainties. However, the design of this algorithm was originally developed for continuous‐time systems. The growth of microcomputers technology has attracted the attention of researchers inside the SM discrete‐time domain. Recently, discretisations schemes for the STA were studied using majorant curves. In this study, the stability analysis in terms of Lyapunov theory is proposed to study a discrete‐time super twisting‐like algorithm (DSTA) for non‐linear discrete‐time systems. The objective is to preserve the STA characteristics of robustness in a quasi‐sliding mode regime that was proved in terms of practical Lyapunov stability. An adequate combination of gains obtained by the same Lyapunov analysis forces the convergence for the DSTA. The problem of state estimation is also analysed for second‐order mechanical systems of n degrees of freedom. Simulation results regarding the design of a second‐order observer using the DSTA for a simple pendulum and a biped model of seven degrees of freedom are presented. [ABSTRACT FROM AUTHOR]

This study presents a novel robust controller strategy for submersible autonomous robotized vehicles (SARV). This controller applies the averaged sub-gradient (ASG) descendant method to optimize the tracking of well-posed reference trajectories. The motion control form of the SARV is done in three stages (cascade-like control design). The phases consist of using the translation velocities as pseudo controllers to adjust the SARV position, regulating the angular velocities to attain the requested translation velocities, and using the proposed ASG to control the thrusters to get the needed angular velocities. ASG implementation optimizes a convex cost function depending on the integral of the tracking error using the ASG method. The application of Barbalat's lemma justifies the tracking error is converging the origin asymptotically. A class of integral sliding mode controllers with a variable state-dependent gain solves the tracking of the designed reference trajectories in each of the three stages. The sliding surface depends on the tracking error for each pseudo-controller, its integral, and the cost function average. The optimization of the cost function can be done without complete knowledge of the SARV dynamics. A numerical example is presented in this study to confirm the suggested control design's effectiveness based on the cost function's time evolution analysis. The forced motion by the proposed controller is compared with the movement obtained by a proportional–integral–derivative (PID) controller. The proposed controller exhibits a better tracking of the reference trajectory than the PID version. • This study presents a robust robust controller for underwater robotic autonomous devices. • An averaged sub-gradient (ASG) descendant control minimizes the trajectory tracking error. • Sub-gradient realization solves an extremum seeking control to stabilize the tracking error. • The controller is of sliding mode type with variable gain based on a state dependent sliding surface. • The dynamic nature of the MRAD regulated by a back-stepping like controller design. [ABSTRACT FROM AUTHOR]

• A class of ISM controllers is proposed to realize the autonomous navigation of UUMV. • The Lagrange equation of the model of the UUMVs is considered to design the online optimization controller based on ISM with ASG of the tracking error norm. • The suggested robust control solves the tracking of reference trajectories in the (x-y-z)-coordinates for the UUMV. • The realized ISM controller with ASG integral term is studied analytically, including the convergence and the rate convergence analysis. • The controller is robust with respect to a wide class of model uncertainties such as the tensor of inertia and non-potential forces (friction, hysteresis, Coriolis, damping, centripetal effects). 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. [ABSTRACT FROM AUTHOR]

This article solves the tracking trajectory problem of teleoperated robotic systems with different workspaces. The overall robotic system satisfies a regular master–slave structure with a delta-robot as the master device and a planar manipulator attached to a Cartesian robot with five degrees of freedom (DOFs) as the slave device. A forward kinematics analysis describes the workspace for the delta-robot and the five-DOFs manipulator. A coordinate transformation based on sigmoidal functions establishes the relation between the workspaces for both robotic devices. The obtained transformation yields a feasible workspace for the slave robot. Then, an inverse kinematics analysis provides the desired reference trajectories. The tracking trajectory control implements a robust strategy based on Barrier Lyapunov functions. The barrier controller does not allow the slave robot to reach non-attainable configurations. State-dependent gains characterized the obtained controller taking into account the different workspaces for each device. Numerical results describe the suggested controller applied in a virtual teleoperated robot and a real robotic system platform. The obtained results confirm the improvements (measured in terms of the mean square error and the l 2 norm of the applied controls) of the proposed controller against a traditional state feedback realization. Furthermore, the results show that the trajectories of the slave robot do not leave the valid workspace. • Output feedback control for teleoperated manipulators under state constraints. • Adaptive control formulation based on logarithmic barrier Lyapunov functions. • Super-twisting differentiator implementation to obtain the tracking error derivative. • Experimental evaluations on a manipulator (slave) and a Delta robot (master). [ABSTRACT FROM AUTHOR]