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This paper deals with, in the framework of absolute stability, boundary stabilization for a nonlinear axially moving beam under boundary velocity feedback controls. The nonlinear boundary control that satisfies a slope-sector condition covering many types of nonlinear control schemes is a negative feedback of the transverse velocity at the right eyelet of the moving beam. Under the nonlinear control scheme, the well-posedness of the nonlinear partial differential equation which depends continuously on the initial value is investigated by means of the Faedo-Galerkin approximation and priori estimates. By exploiting the integral-type multiplier method, the exponential stability of the closed-loop system is established, where a novel energy like function is constructed. The numerical simulation examples using the finite element method are presented to illustrate the effectiveness of the established criterion of the controller.

By integrating the event-based mechanism and the model predictive control (MPC) method, an improved event-based MPC framework is constructed for the nonlinear control problem subject to disturbances. Firstly, a new event-triggering condition is suggested, which is constructed on the basis of the gradients of the differences between the optimal state prediction and the actual one at two consecutive sample times. Then, an event-based MPC algorithm is further proposed, in which the dual-mode control technique is incorporated to handle the nonlinear perturbed system. Furthermore, it is strictly demonstrated that the proposed algorithm will ensure the feasibility of the MPC method and the stability of the considered system, while significantly decreasing the number of solving optimization problems, based on which resources for information transfer can be effectively saved. Finally, simulations and comparisons are shown to verify the efficacy of the proposed framework.

This paper addresses the decoupling control design for the cascaded power electronic transformer (PET) in input-series-output-parallel connection. Due to the coupling and interaction between the sub-modules and between sub-stages, in essence it is a complex nonlinear system. A nonlinear control strategy based on feedback exact linearization (FEL) is developed to decouple all the control objectives so as to realize the dc-link and output voltages fast stabilizing and the submodule balancing without coupling and interactions. Based on the separation of the ac current time-scale and dc voltage time-scale, the FEL control law is derived, and the specific tuning process of control parameters are given for desired control bandwidths. Taken the dynamic influences of the current-loop, filter, and delay into account, further analyses are made and compared with a DAB balancing control-based strategy to show the improvement on decoupling effect and dynamic performance of the proposed control. Finally, the simulation and experimental results verify the theoretical analysis, which exhibit better dynamic features and minimal coupling effect under the condition of bidirectional power changes and parameter inconsistency and uncertainty.

The pneumatic artificial muscle is a kind of flexible actuators used to simulate the characteristics of human muscles. Robots actuated by PAMs possess compliance and safety, which can achieve satisfactory man-machine interaction control. Nevertheless, such robots actuated by PAMs have lots of control problems due to the inherent characteristics, such as hysteresis, creep, high nonlinearities, and so on. Moreover, most existing control methods do not consider constraining overshoots, etc., however, based on safety requirements and actual physical constraints, systems with unconstrained overshoots may have potential risks. A new energy-based nonlinear control method is proposed for 2-link PAM-actuated robots to realize accurate positioning control. First, the dynamic model of 2-link PAM-actuated robots is presented. Further, a new energy storage function is constructed. The overshoots and the terms coupled with control inputs are constrained, which can reduce the unnecessary energy loss while improving the system safety. To our knowledge, the proposed method is the first nonlinear control approach for 2-link PAM-actuated robots, designed and analyzed based upon the original nonlinear dynamics without any linearization, to provide high-performance positioning control with constrained overshoots and eliminated residual oscillations simultaneously. By rigorous analysis, asymptotic stability of the system is proven. Hardware experimental results are presented.

This article investigates the properties, from a nonlinear control system standpoint, of atomic force microscope (AFM) systems, whenever operated in contact mode and controlled in the vertical direction by proportional-integral control law. By modeling the AFM as a system in which a piezo-electric actuator and a cantilever mutually interact in order to produce the sample topography, ensuing distortions affecting the quality of the yielded topography measurement are naturally cast and analyzed. The proposed investigation considers distortions due to the inception of hysteresis and vibrational dynamics within the piezo-actuator or provoked by system saturation. Both hysteresis and saturation are inherently nonlinear phenomena and are modeled as such. In spite of the inherently nonlinear nature of the AFM dynamics, investigations of the contact mode case from a nonlinear standpoint are lacking within the AFM literature. As the topography yielded by the AFM completely relies on its control algorithm, to the point that the measurement itself corresponds to the control action v(t), it becomes of paramount importance to understand how v(t) relates to the actual topography, and how such a relationship is affected by the aforementioned distortions. This article hence intends to contribute to the AFM literature, by providing a study in which the very meaning of the image measurement yielded by the AFM is investigated, in the light of distortions due to nonlinear phenomena. The AFM is considered to be operated in contact mode with a PI algorithm. Furthermore, as a byproduct of the derived nonlinear stability analysis, a novel, model-based algorithm for tuning the PI control gains is provided. Finally, experimental results are presented and analyzed in view of the derived theory.

Autonomous Robots with multiple directional thrusters are normally over-actuated systems that require nonlinear control allocation methods to map the forces that drive the robot’s dynamics and act as virtual control variables to the actuators. This process demands computational efforts that, sometimes, are not available in small robotic platforms. The present paper introduces a new control allocation approach with fast convergence, high accuracy, and dealing with complex nonlinear problems, especially in embedded systems. The adopted approach divides the desired nonlinear system into coupled linear problems. For that purpose, the Real Actions (RAs) and Virtual Control Variables (VCVs) are broke in two or more sets each. While the RA subsets are designed to linearize the system according to different input subspaces, the VCV is designed to be partially coupled to overlap the output subspaces. This approach generates smaller linear systems with fast and robust convergence used sequentially to solve nonlinear allocation problems. This methodology is assessed in mathematical tutorial cases and over-actuated UAV simulations.

This paper presents a novel control strategy for a Dual Active Bridge Series Resonant Converter (DAB-SRC). The strategy seeks to ensure the stability of the converter over its entire dynamic range while enhances the transient response. Both properties allow the use of the converter in new applications where fast dynamics are required, surpassing the performance of existing feedback loops. Starting from the generalized averaged model of the converter, we propose a nonlinear control strategy by means of Lyapunov's stability theory. After that, we derive a series of modifications in order to implement the strategy in a microcontroller or a DSP, including a sensorless method to tackle the lack of measurements of certain variables and an adaptive control law to deal with uncertain parameters in the model. The strategy is evaluated in simulations and experiments, employing a commercial converter and comparing the results with other control policies.

This paper addresses an uncertain nonlinear control system problem with complex state constraints and mismatched uncertainties. A novel Gaussian Mixture Model (GMM) based adaptive PID-Nonsingular Terminal Sliding Mode Control (NTSMC) (GMM-adaptive-PID-NTSMC) method is proposed. It is achieved by combining a GMM based adaptive potential function with a novel switching surface of PID-NTSMC. Next, the stability of the closed-loop system is proved. The main contribution of this paper is that the GMM method is applied to obtain the analytic description of the complex bounded state constraints, ensuring that the states’ constraints are not violated with GMM-based adaptive potential function. The developed potential function can consider the influence of uncertainties. More importantly, the GMM-adaptive-PID-NTSMC can be generalized to control a more representative class of uncertain nonlinear systems with constrained states and mismatched uncertainties. In addition, the proposed controller enhances the robustness, and requires less control cost and reduces the steady state error with respect to the Artificial Potential Function based Nonsingular Terminal Sliding Mode Control (APF-NTSMC), GMM-NTSMC and GMM-adaptive-NTSMC. At last, numerical simulation is performed to validate the superior performance of the proposed controller.

This article studies the robust adaptive asymptotic tracking control problem for uncertain nonlinear systems with event-triggered inputs. Contrary to the existing results, a novel nonaffine nonlinear control input separated design scheme is developed based on the Taylor decoupling technique instead of the previous approximation ways. Correspondingly, the augmented dimension parameter updated laws and the unknown bound estimation of the compounded disturbance with a positive continuous integrable function are skillfully introduced. Also, by introducing a suitable decreasing function of tracking error variables, an improved adaptive event-triggered mechanism is constructed to achieve the asymptotic tracking and the communication load can be effectively alleviated. Moreover, it is shown that all the signals in the closed-loop system are uniformly bounded and the tracking errors converge to zero in a preset compact set. Finally, the validity of the proposed method is illustrated by simulation on an inverted pendulum model.

International audience; In this paper a robust nonlinear Model Reference Adaptive Control (MRAC) is proposed for disturbed linear systems, i.e., linear systems with parameter uncertainties, and external time-dependent perturbations or nonlinear unmodeled dynamics matched with the control input. The proposed nonlinear control law is composed of two nonlinear adaptive gains. Such adaptive gains allow the control to counteract the effects of some perturbations and nonlinear unmodeled dynamics ensuring asymptotic convergence of the tracking error to zero, and the boundedness of the adaptive gains. The nonlinear controller synthesis is given by a constructive method based on the solution of Linear Matrix Inequalities (LMIs). Besides, the simulation results show that, due to the nonlinearities, the rate of convergence of the proposed algorithm is faster than the provided by a classic MRAC.

This paper introduces a Lyapunov-based nonlinear control scheme that mitigates False-Data-Injection (FDI) attacks in real-time for a centralized multi-agent system (MAS) with nonlinear Euler-Lagrange dynamics with additive disturbances and input delays. Since the state tracking error is faulty during FDI attacks, the central controller cannot solely rely on the state tracking error to coordinate the MAS. Therefore, a novel feedback signal is designed to address this challenge and to ensure that the MAS achieves the control objective. The proposed controller combines both learning and model-based approaches to estimate the agents' states and to detect and respond to FDI attacks. A neural network (NN) is used to detect the FDI attacks, where the update laws for the NN weights are designed based on the corresponding stability analysis. Lyapunov-Krasovskii (LK) functionals are used in the Lyapunov-based stability analysis to ensure semi-global uniformly ultimately bounded tracking. A simulation of multi-agent robots with nonlinear Euler-Lagrange dynamics is provided, demonstrating the promising performance of the developed method to respond to FDI attacks.

This paper presents a new active controller technique effect of functionally graded (FG) cylindrical shell structure model within joint harmonic and parametric excitations. The new active controller involves Nonlinear Proportional-Derivative (NPD) plus Negative Cubic Velocity Feedback (NCVF) as a new nonlinear control method (NPDCVF). The motivation of this study is the well-known observation that NPDCVF control method can offer a means to improve the performance of plant systems. The coupled nonlinear differential equations with two modes have been derived applying the von Karman nonlinear theory, Galerkin’s process, and the static condensation technique. Static condensation is the process of decreasing the number of free displacements or degrees of freedom. We have added other three different controller methods over the structure to select the best controller. The three applied controller methods to the considered structure are: Integral Resonant Control (IRC), Positive Position Feedback (PPF), and Nonlinear Integral Positive Position Feedback (NIPPF) which are applied to the considered structure. We establish that the best one for dipping the high vibration amplitudes is the NPDCVF as a new controller. The perturbation technique is useful to solve the present model including quadratic and cubic nonlinearities subjected to mixed harmonic and parametric forces within the simultaneous primary resonance case ( Ω = ω 1 , Ω = ω 2 ) as the worst resonance case of the system. All numerical outcomes have been completed with the help of MATLAB Ra 18.0 program software over the investigated model. The obtained results have proved that this new controller is excellent for improving the structure by reducing the risky vibrations caused during primary resonances. Frequency response equations have helped in observing the stability examination of the obtained numerical solutions. The actions of several factors performed on the controlled model have been examined and described. Some comparisons have also been prepared with the available recent published papers of a similar model.

The paper describes a novel method of sampled-data in space (spatial variable) nonlinear control of scalar semilinear parabolic and hyperbolic systems with unknown parameters, distributed disturbances and finite number of measurements along the spatial variable. Differently from recent results based on piecewise constant control laws, the proposed one is used piecewise nonlinear functions choosing by designer for providing some properties in the closed-loop system. In particular, we propose several types of functions providing reduced control. The gain design in the control law is found as a solution of linear matrix inequalities with minimum ultimate bound guarantee. The simulations confirm theoretical results and show the efficiency of the proposed control scheme compared with some existing ones.

This paper presents an improved backstepping control scheme with the adaptive estimation for nonlinear missile systems. First, the inherent nonlinearities and large uncertainties caused by high ang...

Solar thermal plants are commonly constituted of different subsystems, such as the solar collector field, accumulation tanks, and gas heaters, to enhance plant performance. Nevertheless, from a process control perspective, the changes in the subsystem's configuration can cause interactions and compromise the controller performance. Therefore, this work proposes a hybrid practical nonlinear predictive control for a solar thermal plant facility, aiming to improve the plant operation performance by considering mixed-logical dynamic models and including the process constraints as linear mixed-integer inequalities in a single control layer. The proposed strategy is compared with the conventional practical nonlinear control with an external decision-maker. Both frameworks are simulated under actual process circumstances using real meteorological data and validated hybrid models of the CIESOL facility (Spain). This paper makes relevant contributions in some aspects. From the control framework perspective, a new formulation of the hybrid control algorithm simplifies the control structure, excluding the decision-maker structure from its task. Moreover, the present study considers variations in load demand, a novel and significant contribution. The results demonstrate that the hybrid nonlinear controller performs better than the conventional approach, with a reference tracking error index approximately 35% lower in a sunny day scenario.

Fault characteristics analysis normally provides a theoretical foundation for the protection design. Although conventional fault analysis of inverter-interfaced renewable energy sources (IIRESs) can characterize post-fault steady-state at the power frequency, it might not effectively present the fault transient. This can negatively affect the protection based on fault transient data within 20–30 ms after a grid fault. Thus, the fault transient of IIRESs needs to be fully investigated. Given this, the nonlinear effect of controller saturation is considered in this study. The domain of attraction (DOA) is first established to estimate the practical working state of the controller within the current loop. The transient fault current (TFC) analytical model is then proposed in accordance with the nonlinear control response of the controller under different working stages, which reveals a detailed transient transition of the fault current. Meanwhile, the proposed model is low-order and presents high applicability in different fault scenarios. Simulation results indicate that the TFC analytical accuracy obtained using the proposed method is improved by at most 50% relative to the accuracy reported in published studies. Field short-circuit test data are ultimately used to verify the performance of the proposed TFC analytical model.

A robust nonlinear control based only on position measurements to compensate for the strong hysteresis nonlinearity in a piezoelectrically actuated robotic hand is proposed. Based on a high-gain observer to estimate the hysteresis response and nonlinear control law, locally exponential stable results are obtained. The observer and controller are arranged to conform to an output-feedback scheme, which is simple to implement and does not require additional computation as soon as the model parameters are identified and known. The proposed control technique is valuable for hysteresis that is modeled with the classical Bouc-Wen model. The results provide a closed-loop system that is robust under external disturbances in all the system states. Simulations show the effectiveness of the approach.

In this paper, an antidisturbance controller is presented for helicopter stochastic systems under disturbances. To enhance the antidisturbance abilities, the nonlinear disturbance observer method is applied to reject the time-varying disturbances. Then, the antidisturbance nonlinear controller is designed by combining the backstepping control scheme. And the stochastic theory is used to guarantee that the closed-loop system is asymptotically bounded in mean square while the proposed control method is shown via some traditional nonlinear control techniques, which still show some common issues such as “dimension explosion” or others. The result of this paper can be regarded as a typical case of the nonlinear control method to help and promote the generation of advanced methods.

In this study, an electronic model of a memristive-based 4D autonomous chaotic system with a line equilibrium is proposed. A memristor offers many advantages because of its superior properties for improving different circuits, e.g., chaotic circuits and systems. In particular, its nonlinearity and nonvolatile behavior provide a unique opportunity to design chaotic circuits. Therefore, we designed a flux-controlled memristor-based 4D autonomous chaotic system having a line equilibrium. The fundamental dynamical properties of the system are demonstrated with regards to equilibrium, Jacobian matrices, Lyapunov exponents, and bifurcation behavior. A nonlinear controller based on the Lyapunov stability method was also designed to control the novel system. Furthermore, it is controlled by only one state controller. As was expected, both theoretical and simulation results of the 4D chaotic oscillator were in good agreement with the experimental results.

Wavetubes are employed for measurements of acoustic properties in various fluids. The ability to manipulate and control the frequency-dependent boundary impedance of the tube improves the estimation accuracy. Passive solutions, which use composite materials to change the boundary impedance, enable one to realize a finite combination of boundary impedances. In this paper, the tube boundary impedance is tuned at will by using two loudspeakers. The suggested method operates in the presence of dispersion by estimating, in real-time, a parametric reduced-order model using a multichannel least mean square algorithm. The identified model is fed to a nonlinear, adaptive control algorithm to realize modal traveling wave ratio (TWR) control. It has been noted that the TWR is smooth and parabolic across closed regions in the parameter space, thus assuring the convergence of the nonlinear control. Several methods to estimate the TWR gradient are considered and compared based on an analytical model of a rigid impedance tube. An experimental case study utilizing an air-filled impedance tube with two loudspeakers is presented. The results demonstrate the ability to control the dynamics of the principal acoustic mode at will, thus enabling one to set the desired tube's boundary impedance.

As an important component of microgrid system, the grid-connected inverter is composed of power electronic devices, which makes the system lack physical inertia and exhibit low output impedance. Especially in the transition process of grid connection, a large current impact will be generated, which may make the system unstable. Therefore, in response to these problems, a nonlinear control method is proposed that enables the grid-connected inverter to switch freely between grid-connected mode and island mode. The linear control part introduces the mechanical equations of the rotor of the synchronous motor, which has virtual inertia and damping, and at the same time derives the corresponding mathematical model. As regards the nonlinear control part, the nonlinear controller is designed by integrating the integral sliding mode control method and backstepping control method. Meanwhile, considering the uncertainties including external disturbances, measurement errors and modelling errors, an observer based on the radial basis function neural network (RBFNN) is proposed to estimate the uncertainties to offset their influence. Then, the stability of the control system is proved by Lyapunov stability criterion. Finally, the simulation results prove that the proposed control scheme can realize the stability of the microgrid system in several operation modes and ensure the sound dynamic performance with quick response comparing with other nonlinear control methods.

This paper presents an input–output linearization (IOL) control strategy to achieve PFC (power factor correction) and output voltage constant in a boost converter. The method transforms the nonlinear system to a linear one in new coordinates by the appropriate nonlinear coordinate transformation and state feedback, ultimately allowing the controller to be designed according to the classical linear control theory. An example implementation is simulated using PSIM software. The simulation results show that the phases of input voltage and input current are consistent, and the output voltage remains constant under load step changes. A set of experimental devices are set up to verify the control method, and the results are consistent with the simulation. Thus, the method is proved to be effective in achieving PFC and provides robust constant voltage output in the boost converter.

We propose a new framework to design controllers for high-dimensional nonlinear systems. The control is designed through the iterative linear quadratic regulator (ILQR), an algorithm that computes control by iteratively applying the linear quadratic regulator on the local linearization of the system at each time step. Since ILQR is computationally expensive, we propose to first construct reduced-order models (ROMs) of the high-dimensional nonlinear system. We derive nonlinear ROMs via projection, where the basis is computed via balanced truncation (BT) and LQG balanced truncation (LQG-BT). Numerical experiments are performed on a semi-discretized nonlinear Burgers equation. We find that the ILQR algorithm produces good control on ROMs constructed either by BT or LQG-BT, with BT-ROM based controllers outperforming LQG-BT slightly for very low-dimensional systems.

For a continuous nonlinear control system on a finite time interval with control constraints, where the right-hand side of the dynamics equations is linear in control and linearizable in the vicinity of the zero equilibrium position, we consider the construction of a feedback according to the Kalman algorithm. For this, the solution of an auxiliary optimal control problem with a quadratic functional is used by analogy with the SDRE approach.Since this approach is used in the literature to find suboptimal synthesis in optimal control problems with a quadratic functional with formally linear systems, where all coefficient matrices in differential equations and criteria can contain state variables, then on a finite time interval it becomes necessary to solve a complicated matrix differential Riccati equations, with state-dependent coefficient matrices. This circumstance, due to the nonlinearity of the system, in comparison with the Kalman algorithm for linear-quadratic problems, significantly increases the number of calculations for obtaining the coefficients of the gain matrix in the feedback and for obtaining synthesis with a given accuracy. The proposed synthesis construction algorithm is constructed using the extension principle proposed by V. F. Krotov and developed by V. I. Gurman and allows not only to expand the scope of the SDRE approach to nonlinear control problems with control constraints in the form of closed inequalities, but also to propose a more efficient computational algorithm for finding the matrix of feedback gains in control problems on a finite interval. The article establishes the correctness of the application of the extension principle by introducing analogs of the Lagrange multipliers, depending on the state and time, and also derives a formula for the suboptimal value of the quality criterion. The presented theoretical results are illustrated by calculating suboptimal feedbacks in the problems of managing three-sector economic systems.

In this paper, a nonlinear predictive generalized minimum variance (NPGMV) controller is proposed and explicitly formulated for a class of nonlinear systems modeled by autoregressive second-order Volterra series, applying the polynomial approach. Hence, a new benchmark controller for performance assessment is introduced to improve the achievable control performance. Furthermore, to have an efficient control assessment, a data-driven algorithm based on the NPGMV control is presented that uses only the closed-loop operating data. In the design procedure, a multi-step cost function is defined to incorporate predictive action. Exploiting the predictive control concept enables the control scheme to handle constrained problems. Also, the proposed control algorithm utilizes an inherent integrating effect, which is essential for practical purposes. Volterra series are employed for modeling and identification of the nonlinear processes, using conventional least-squares methods. To show the effectiveness of the proposed methodology, simulation results and comparison studies are provided on a cascade Wiener model and a continuous stirred tank reactor (CSTR) chemical pilot plant. Finally, an experimental study on a pressure pilot plant is used to demonstrate the applicability of the proposed control scheme. The simulation and experimental results indicate satisfactory performance of the proposed controller.

In this article, the problem of flight control for a two-degree-of-freedom helicopter system is studied. Since the helicopter is a multiinput, multioutput nonlinear control system, a Takagi–Sugeno (T–S) fuzzy model is applied to approximate the system. All submodels of the new T–S fuzzy model contain constant terms due to the nonlinear characteristics of the helicopter system. In this article, sampled-data control is considered and the sampled data are transmitted to the system over a communication network. A large amount of sampled data transmitted over the network can significantly increase the computational and communication burdens for the network with a limited bandwidth. To overcome this difficulty, an event-triggered mechanism is introduced. In order to validly control the T–S fuzzy system, a fuzzy proportional integral-derivative (PID) controller is designed based on the Lyapunov method and practical stability criteria, which are obtained by using improved integral inequalities and the linear matrix inequality technique. Finally, a numerical example is given to show the effectiveness of the obtained results.

The d-restricted dynamic observer error linearization (RDOEL) problem of the general nonlinear control system is to find a restricted auxiliary dynamic system of dimension d such that the extended control system is state equivalent to a nonlinear observer canonical form. The autonomous version of the RDOEL problem can be found in the literature. In this paper, the vector fields are defined with parameter u and geometric necessary and sufficient conditions for RDOEL problem of the general (i.e. non-affine) nonlinear system are given. Our conditions with $$d=0$$ also give the geometric necessary and sufficient conditions for the state equivalence of a general nonlinear control system to a nonlinear observer canonical form (NOCF) with output transformation (OT). Since our proofs are constructive, an extended state transformation can be found in the theorems. The conditions are simple and thus can be implemented by a MATLAB program.

Purpose The purpose of this paper is to report on the global practical uniform h-stabilization for certain classes of nonlinear time-varying systems and its application in a separately excited DC motor circuit. Design/methodology/approach Based on Lyapunov theory, the practical h-stabilization result is derived to guarantee practical h-stability and applicated in a separately excited DC motor. Findings A controller is designed and added to the nonlinear time-varying system. The practical h-stability of the nonlinear control systems is guaranteed by applying the appropriate controller based on Lyapunov second method. Another effective controller is also designed for the global practical uniform h-stability on the separately excited DC motor with load. Numerical simulations are demonstrated to verify the effectiveness of the proposed controller scheme. Originality/value The introduced approach is interesting for practical h-stabilization of nonlinear time-varying systems and its application in a separately excited DC motor. The original results generalize well-known fundamental result: practical exponential stabilization for nonlinear time-varying systems.

In this paper, a method of designing control inputs for stochastic nonlinear processes under state-feedback is proposed. The objective is to determine a control input that minimizes the expected value of the integral of error between the set-point and the states. Since the states may not be measured, they are estimated using a particle filtering algorithm. The optimal control design is then reformulated as a parameter estimation problem using control vector parameterization where the inputs are considered as a nonlinear function of the error between the state estimates and the set-point. The parameters are then computed through a homotopy based optimization method. The control performance resulting from proposed homotopy based optimization method is compared with that of direct optimization and an existing nonlinear control method on a Solid Oxide Fuel Cell (SOFC) stack model.

This paper investigates the model-based nonlinear control of a class of soft continuum pneumatic manipulators that bend due to pressurization of their internal chambers and that operate in the presence of disturbances. A port-Hamiltonian formulation is employed to describe the closed loop system dynamics, which includes the pressure dynamics of the pneumatic actuation, and new nonlinear control laws are constructed with an energy-based approach. In particular, a multi-step design procedure is outlined for soft continuum manipulators operating on a plane and in 3D space. The resulting nonlinear control laws are combined with adaptive observers to compensate the effect of unknown disturbances and model uncertainties. Stability conditions are investigated with a Lyapunov approach, and the effect of the tuning parameters is discussed. For comparison purposes, a different control law constructed with a backstepping procedure is also presented. The effectiveness of the control strategy is demonstrated with simulations and with experiments on a prototype. To this end, a needle valve operated by a servo motor is employed instead of more sophisticated digital pressure regulators. The proposed controllers effectively regulate the tip rotation of the prototype, while preventing vibrations and compensating the effects of disturbances, and demonstrate improved performance compared to the backstepping alternative and to a PID algorithm.

In this article, a novel robust observer-based nonlinear control approach is proposed for quadrotors with unmodeled dynamics and external disturbances, wherein the tracking errors are restricted effectively. Two nonlinear disturbance observers are proposed to deal with uncertainties in the inner and outer loops, respectively. On this basis, a robust observer-based nonlinear control approach is put forward for quadrotor systems. Specifically, in the outer loop subsystem, a robust observer-based control scheme is proposed, which can reduce unexpected tracking errors for quadrotors effectively. Subsequently, based upon the geometric methods, the coordinate-free attitude controller and the nonlinear disturbance observer are integrated as a robust controller in the inner loop subsystem. Based upon full nonlinear dynamics, the solutions of the closed-loop system are proven to be uniformly ultimately bounded by means of rigorous Lyapunov analysis. A series of comparative experiments consisting of the implementation of a nonlinear proportional-integral-derivative (PID)-type controller, an observer-based sliding mode controller, and the proposed controller are conducted to demonstrate the remarkable performance of the proposed method in terms of higher tracking accuracy and stronger robustness.

The survey examines the current state of the speed gradient method, developed in the 1970–80s for synthesizing control and adaptation algorithms in nonlinear systems, as well as numerous applications of the method to solving scientific and engineering problems. Brief information about speed gradient algorithms and conditions of their applicability, optimality, and passivity are given. Applications of the method to problems of adaptive control and identification, nonlinear control, energy and nonlinear oscillation control, and control in network, multiagent, and distributed systems are discussed. Applications of the method to control of technical systems and to problems in physics, biology, and ecology are presented. Modern modifications and generalizations of the method are provided, including non-Euclidean speed gradient algorithms based on Lyapunov–Bregman functions.

For stochastic strict-feedback nonlinear systems with unknown parameters in the drift terms or the diffusion terms, we develop new least-squares identification schemes without regressor filtering. A key new ingredient in the proposed estimator design is a weighted term with design parameters, which is introduced to deal with the nonlinear terms and stochastic noise. With such an estimator, new adaptive controllers are designed to guarantee that the equilibrium at the origin of the closed-loop system is globally stable in probability, and the states are regulated to zero almost surely. Besides, by suitably selecting the estimator parameters, we prove that the proposed least-squares estimators are convergent, as well as strongly consistent in some special cases. Finally, two simulation examples are given to illustrate the least-squares identification and the adaptive control design.

To date, most control strategies have been designed for the two-dimensional and three-dimensional overhead crane systems with the single pendulum effect. In fact, three-dimensional overhead crane systems often exhibit the double-pendulum effect in practical applications, which is more controlled than the general single-pendulum crane, and also makes the controller design more challenging. This paper proposes a new nonlinear control strategy that enhances the coupling between the trolley speed and the swing angle components. Specifically, we devise a new energy-like function by introducing two generalized signals that can reflect the trolley speed and the hook and load swing angle components. This strategy greatly improves the effectiveness of the transient control process. Meanwhile, the asymptotic stability of the closed-loop system is not only guaranteed, but also the desired position of the trolley and swing angle suppression are achieved using the control strategy.

In this work, we explore multi-input multi-output (MIMO) nonlinear control systems design by generalizing concepts from radio link analysis. We demonstrate practical applications of multidimensional sampling and reconstruction to reducing computational overhead in nonlinear systems analysis. Using multi-spectral analysis, we show that (de)fuzzification in control systems and (de)modulation in communication systems are analogous. Finally, we explore the values of fuzzy submodels as quantum mechanics objects for stability analysis and feedback controller synthesis of nonlinear mechanical systems. The effectiveness of the proposed approach is confirmed by simulating the attitude model a telecommunications satellite.

Source optimisation (SO) is an approved approach to improve the imaging quality in inverse lithography techniques. It is critical to apply an optimisation approach with high convergence efficiency and minimum errors in pixel-based SO. To improve the convergence efficiency of the pixel-based SO, a route of particle swarm optimiser (PSO) combined with the adaptive nonlinear control strategy (ANCS) is proposed in this study. As a global optimisation algorithm, ANCS-PSO has the attributes of breaking away from the local optimum by adjusting the particle learning factor adaptively. In addition, the nonlinear control approach can broaden the search range and speed up the convergence of the iteration operation. The proposed approach also is compared with the linear decreasing inertia weight strategy and the simulated annealing strategy. The performance verification simulation displays the validity of PSO-ANCS and its potentials in SO with high convergence efficiency and optimisation capacity, by comparing the linear decreasing inertia weight strategy and the simulated annealing strategy.

Abstract We consider a nonlinear control system with a bang-bang hysteresis control, which is a simplified model of a thermal energy harvester. We obtain conditions on the controller and the system parameters guaranteeing the existence of a periodic mode in the system.

In this paper, we devoted to deal with the rotational periodic problem of some fractional iterative systems in the sense of Caputo fractional derivative. Under one sided-Lipschtiz condition on nonlinear term, the existence and uniqueness of solution for a fractional iterative equation is proved by applying the Leray-Schauder fixed point theorem and topological degree theory. Furthermore, the well posedness for a nonlinear control system with iteration term and a multivalued disturbance is established by using set-valued theory. The existence of solutions for a iterative neural network system is demonstrated at the end.

In this article, we propose a new approach to design globally convergent reduced-order observers for nonlinear control systems via contraction analysis and convex optimization. Despite the fact that contraction is a concept naturally suitable for state estimation, the existing solutions are either local or relatively conservative when applying to physical systems. To address this, we show that this problem can be translated into an offline search for a coordinate transformation after which the dynamics is (transversely) contracting. The obtained sufficient condition consists of some easily verifiable differential inequalities, which, on one hand, identify a very general class of “detectable” nonlinear systems, and on the other hand, can be expressed as computationally efficient convex optimization, making the design procedure more systematic. Connections with some well-established approaches and concepts are also clarified in this article. Finally, we illustrate the proposed method with several numerical and physical examples, including polynomial, mechanical, electromechanical, and biochemical systems.

This paper focuses on the adaptive event-triggered consensus control problem for a class of stochastic nonlinear multi-agent systems with unknown nonlinear control directions and external disturbances. The heterogeneous nonlinear dynamics and non-identical unknown control directions are discussed for different agents. The application of the event-triggered mechanism can effectively decrease the update frequency of the controller, and unknown nonlinear dynamics are solved by using fuzzy logic systems. Under the action of the designed distributed controller, all signals of this stochastic multi-agent systems can reach semi-globally uniformly ultimately bounded (SGUUB) in mean square. Furthermore, Zeno behavior can be ruled out by the existence of positive inter-event intervals. Finally, a simulation example is presented to verify the feasibility of the algorithm.

The ship motion system is a nonlinear control object, and its system parameters exhibit time-varying characteristics with the ship motion state, which increases the difficulty of control. Therefore, parameter identification has an important significance for the stability of ship motion control. Aiming at the real-time identification problem of the nonlinear and time-varying ship motion system during movement, this paper reconstructs the ship motion system with the propeller speed and rudder angle as control variables and designs an online identification algorithm with the sliding time window method based on the extended Kalman filter algorithm. In addition, to solve the problem of noise in ship motion data collected in real-time, a real-time wavelet filter is developed to perform online preprocessing of the input data of the identification algorithm. The applicability of the method is further demonstrated via a model-scale Korea Research Institute of Ships and Ocean Engineering container ship free-running experiments in a basin.

Nonlinear control of turbofan engines in the flight envelope has attracted much attention in consideration of the inherent nonlinearity of the engine dynamics. Most nonlinear control design techniques rely on the correction theory of reference model parameter to extend the typical flight operations from ground operation. However, dynamic uncertainties in flight envelope lead to the deviation of operating state, and it is negative to control performance. This article is to develop online correction neural network–based speed control approaches for the turbofan engine with dynamic uncertainty in the flight envelope. Two improved online correction nonlinear ways combined with nonlinear autoregressive moving average (NARMA) are proposed, such as gradient search nonlinear autoregressive moving average with feedback linearization (NARMA-L2) control and iterative learning NARMA-L2 control. The contribution of this article is to provide better control quality of fast regulation and less steady errors of engine speed by the proposed methodology in comparison to the conventional NARMA-L2 control. Some important results are reached on both turbofan engine controller design and dynamic uncertainty tolerance at the typical flight operations, and the numerical examples demonstrate the superiority of the proposed control in the flight envelope.

This article addresses theoretical and practical challenges associated with a commercially available and ready-to-fly small-scale unmanned aircraft system (UAS) developed by Parrot SA: the Mambo quad rotorcraft. The dynamic model and the structure of the controller running onboard the UAS autopilot are not disclosed by its manufacturers. For this reason, a novel robust controller for discrete-time systems under time delays and input saturation is first developed for this platform. Then, three fundamental estimation and control challenges are addressed. The first challenge is the system identification of the $X$ and $Y$ translational dynamics of the UAS. To accomplish this goal, input–output data pairs are collected from different UAS platforms during real-time experimental flights. A group of dynamic models are identified from the data pairs through an extended least-squares algorithm. The obtained models are similar in nature but exhibit parametrical variations due to uncertainties in the fabrication process and different levels of wear and tear. Using a time-varying modeling approach, the second challenge addresses the development of a robust controller, which guarantees the stability of all the identified dynamic models. The third challenge addresses the development of a nonlinear controller enhanced with a perturbation estimation, which can reject, from the nominal model, the effects of model uncertainties and perturbations. These theoretical developments are presented in the form of two original theorems. The proposed strategies are ultimately validated in a set of real-time experiments, demonstrating their effectiveness and applicability.