Nonstrict-feedback Form Research Articles

Adaptive Fuzzy Output Feedback Control for High-Order Switched Systems with Fuzzy Dead Zone

In this paper, an observer-based adaptive control problem for a class of high-order switched nonlinear systems in non-strict feedback form with fuzzy dead zone and arbitrary switchings is investigated. Fuzzy logic system was utilized to model the unknown nonlinear function with the universal approximation ability. An adaptive high-order observer is constructed to estimate unavailable state variables. The effect of dead zone can be eliminated by a Nussbaum function. By using the Lyapunov stability theory and backstepping design procedure, the proposed adaptive controller can guarantee all the variables in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB). Simulation results are exhibited to demonstrate the effectiveness of the proposed control scheme.

Observer-based adaptive neural optimal control for discrete-time systems in nonstrict-feedback form

This paper considers the problem of observer-based adaptive near-optimal control for a class of nonstrict-feedback discrete-time nonlinear systems with non-symmetric dead zone. In order to compensate the effect of dead-zone on the control performance, an adaptive auxiliary signal is constructed to estimate the unknown dead-zone parameters. For the unknown nonlinear functions, neural networks (NNs) are introduced to identify them and to estimate the unknown parameters. To resolve the difficulty resulting from the unavailable state variables, an NN-based observer is designed. Moreover, according to the framework of adaptive control, a novel reinforcement learning algorithm is developed to guarantee that the near-optimal control performance is achieved. Finally, some simulation results are provided to illustrate the effectiveness of the proposed control algorithm.

Fuzzy Adaptive Practical Finite-Time Control for Time Delays Nonlinear Systems

This paper focuses on fuzzy adaptive practical finite-time output feedback control problem for a class of single-input and single-output nonlinear system with time-varying delays in nonstrict feedback form. Fuzzy logic systems are adopted to approximate the unknown nonlinear functions, and state observer is constructed to estimate the unmeasured states. By combining practical finite-time Lyapunov stability theory with the backstepping design, an observer-based fuzzy adaptive practical finite-time control strategy is proposed. Meanwhile, the stability of the closed-loop system is proved, which means that the output can follow the given reference signal in a finite time, and the closed-loop system is semi-global practical finite-time stability. Finally, two simulation examples are provided to elaborate the effectiveness of the presented control strategy.

Cooperative adaptive finite‐time control for stochastic multi‐agent systems with input quantisation

In this study, the finite-time cooperative tracking issue for non-linear multi-agent systems with stochastic disturbances is addressed. Different from the existing asymptotical stable control, the finite-time cooperative control can ensure the outputs of agents reach agree in finite time by raising a novel finite-time stability criterion. The radial basis function neural networks are employed to cope with the unknown non-linearities caused by the non-linear non-strict feedback form. Moreover, this study designs a new adaptive quantised control strategy to reduce communication burden. With such a control scheme, the tracking errors converge to a small area of the origin in finite time. Finally, some numerical simulation results are presented to testify the effectiveness of the approach proposed in this study.

Adaptive tracking control for switched nonlinear systems with fuzzy actuator backlash

This paper concentrates on the adaptive tracking control problem for a class of switched nonlinear systems in nonstrict-feedback form with uncertain actuator backlash. The switching signal considered in our model is arbitrary. The adaptive tracking controller design procedure is divided into three parts. Firstly, a novel fuzzy backlash model is presented to describe the uncertain backlash. Then, the fuzzy backlash is defuzzified and approximated by the linear combination of a linear term and a disturbance-like term without constructing a backlash inverse. Finally, an adaptive backstepping-based tracking controller via common Lyapunov function (CLF) method is presented to guarantee the tracking error asymptotically converges to an adjustable region of zero. The stability analysis and simulation examples are presented at the end of this paper to further verify effectiveness of our control scheme.

Observer-Based Adaptive Fuzzy Fault-Tolerant Control for Stochastic Nonstrict-Feedback Nonlinear Systems With Input Quantization

This paper is focused on the observer-based adaptive fuzzy control problem for nonlinear stochastic systems with the nonstrict-feedback form, in which some complicated and challenging issues including unmeasurable states, input quantization and actuator faults are addressed. The fuzzy logic systems are introduced to approximate the nonlinear functions existing in the control system. A fuzzy observer is designed to observe the unavailable state variables. In order to handle the negative effects resulting from input quantization and actuator faults, a damping term with the estimation of unknown bounds as well as a positive time-varying integral function are constructed, respectively. Furthermore, an observer-based adaptive fuzzy control scheme is proposed for the considered systems to compensate for the effects of input quantization and actuator fault based on adaptive backstepping approach. The proposed control strategy can guarantee that all the signals in the closed-loop system are bounded. Finally, simulation results are provided to illustrate the effectiveness of the proposed adaptive control scheme.

Sampled-data control of a class of switched nonlinear systems under asynchronous switching

This paper focuses on an output feedback stabilization problem for a class of switched nonlinear systems in non-strict feedback form under asynchronous switching via sampled-data control. Since the output of the considered systems is measurable only at the sampling instants, an observer is designed with a tunable scaling gain to estimate the state, and then a sampled-data controller is constructed with the sampled estimated state. As a distinctive feature, a merging virtual switching signal is introduced to describe the asynchronous switching generated by detecting the activation of the subsystem. By choosing an appropriate Lyapunov function, it is proved that the constructed controller with dwell time constraint can globally stabilize the considered systems under asynchronous switching. Finally, the effectiveness of the proposed method is illustrated by two examples.

Finite Time Controller Design of Nonlinear Quantized Systems with Nonstrict Feedback Form

This article considers a finite-time control problem of nonlinear quantized systems in complex environments. The controlled system is in a non-strict feedback form. By applying a nonlinear decomposition of hysteretic quantizer, the quantization issue is tackled successfully. By employing a structural property of radial basis function (RBF) neural networks (NNs), the conventional backstepping method is extended to non-strict feedback nonlinear quantized systems. Based on the finite time stability criterion, a new adaptive neural control scheme is presented. The constructed neural controller can ensure the transient performance of nonlinear quantized systems.

Adaptive Finite-Time Control of Nonlinear Quantized Systems With Actuator Dead-Zone

This paper investigates a finite-time control problem of nonlinear quantized systems with actuator dead-zone in a non-strict feedback form. By combining a simplified dead-zone model and the sector-bound characteristic of a hysteretic quantizer, the control difficulties caused by the coexistence of unknown actuator dead-zone and control signal quantization effect are overcome. By applying the approximation ability of neural network systems, an novel neural adaptive controller is constructed, which can compensate the unknown control gain. The designed neural controller can ensure the transient performance of nonlinear quantized systems with actuator dead-zone in finite-time. Based on the Bhat and Bernstein theorem, the finite-time stability of system is proved. Finally, a numerical example is given to verify the validity of the proposed approach.

Neural Networks-Based Adaptive Tracking Control for a Class of High-Order Stochastic Nonlinear Time-Delay Systems

In this paper, neural networks (NNs)-based adaptive backstepping control problem is investigated for uncertain high-order stochastic nonlinear time-delay systems in nonstrict-feedback form. The control design problems appeared in our considered system are (1) high-order nonstrict-feedback structure; (2) completely unknown nonlinear functions; (3) full-state time delays; and (4) stochastic disturbances. The NNs are directly utilized to cope with the completely unknown nonlinear functions and stochastic disturbances existing in systems. The problem raised by full-state time delays is addressed by combining the appropriate Lyapunov-Krasovskii functional with hyperbolic tangent functions. In addition, the variable separation technique is employed to handle the nonstrict-feedback structure of the system. At last, on the basis of stochastic Lyapunov function method, an adaptive neural controller is developed for the considered system. It is shown that the designed adaptive controller can guarantee that all the signals remain semi-globally uniformly ultimately bounded (SGUUB) and the desired signal can be tracked with a small domain of the origin. The simulation results are offered to illustrate the feasibility of the newly designed control scheme.

Adaptive Neural Tracking Control of Nonlinear Nonstrict-Feedback Systems With Unmodeled Dynamics

In this paper, an adaptive neural control approach for a class of nonstrict-feedback nonlinear systems with unmodeled dynamic is presented. During the controller design process, the main difficulties arise from unknown functions and unmodeled dynamics, which are inevitable in practical applications. The unknown functions are approximated by utilizing the radial basis function neural networks' (RBF NNs) method, and for the problem of the unmodeled dynamics, a dynamic signal is introduced. The innovation of this paper is that we use the property of Gaussian functions to deal with the nonstrict-feedback form. Based on the above precondition, an adaptive NNs controller design scheme is developed by applying the backstepping recursive design. The proposed adaptive control approach guarantees that all the signals in closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error converges to a small neighborhood around the origin by choosing appropriate parameters. In the end, a simulation example is provided to demonstrate the effectiveness of the proposed method.

Adaptive Neural Fault-Tolerant Control for a Class of Stochastic Switched Nonlinear Systems

This paper addresses the adaptive neural fault-tolerant control (FTC) problem for a class of stochastic switched nonstrict-feedback nonlinear systems, which have actuator faults that incorporate loss of effectiveness, stuck, and outage. Based on the character of the Gaussian function, the problem of nonstrict-feedback form is solved well. In the process of designing the controller, neural networks (NNs) are utilized to estimate the unknown functions. The problem of actuator faults is handled by designing the FTC method that is obtained by introducing a smooth function and backstepping technique. Then, the control effect satisfies that all the signals in the resulting closed-loop system are bounded and the tracking error converges to a small neighborhood around the origin. To illustrate the high efficiency of the proposed control method, a vivid simulation example is given in the end.

Fuzzy Adaptive Control Design Strategy of Nonlinear Switched Large-Scale Systems

The decentralized adaptive fuzzy control problem for switched nonstrict-feedback nonlinear large-scale systems is investigated in this paper. Fuzzy logic systems are adopted to identify the unknown nonlinear system functions and unknown interconnected nonlinearities. A linear state observer is designed to solve the problem of unmeasured states, and a new observer-based output-feedback decentralized control scheme is developed based on adaptive fuzzy control principle and bacsktepping design technique. The proposed control strategy not only solves the control design problem of more general form nonlinear switched systems in nonstrict-feedback form, but also does not require the switched signals to meet the restriction of average dwell time. The stability of fuzzy control systems under arbitrary switchings is proven based on the common Lyapunov function method. Simulation results of numerical examples are presented to further demonstrate the effectiveness of the proposed control strategy.

Finite-Time Filter Decentralized Control for Nonstrict-Feedback Nonlinear Large-Scale Systems

This paper solves the finite-time decentralized control problem for uncertain nonlinear large-scale systems in nonstrict-feedback form. The considered controlled plants are different from the previous results of finite-time control systems, which are the nonstrict-feedback large-scale systems with the unknown functions consisting of all states, interactions, and immeasurable states. Fuzzy logic systems and a filter-based state observer are utilized to model uncertain systems and deal with the immeasurable states, respectively. By combining the backstepping recursive design with Lyapunov function theory, a finite-time adaptive fuzzy decentralized control approach is raised. It is testified that the developed control strategy can guarantee that the closed-loop signals are bounded, and the outputs of systems have satisfactory tracking performance in a finite time. A quadruple-tank process system is given to testify the effectiveness and applicability of the proposed approach.

Global sampled-data output feedback stabilization for a class of stochastic nonlinear systems with time-varying delay

This paper studies the global sampled-data output feedback stabilization problem for a class of stochastic nonlinear systems. The considered system is in non-strict feedback form with unknown time-varying delay. A state observer is introduced to estimate the unmeasured states. With the help of the backstepping method, a linear sampled-data output feedback controller is constructed. By choosing an appropriate Lyapunov–Krasoviskii functional and an allowable sampling period, it is shown that the stochastic system can be globally asymptotically stabilized in the mean square sense under the developed control scheme. Finally, two examples are presented to verify the effectiveness of the designed control scheme.

Global practical stabilisation of a class of switched nonlinear systems via sampled-data control

ABSTRACT This paper investigates a global practical stabilisation problem of a class of switched nonlinear systems via sampled-data control, where all the subsystems are assumed to be in non-strict feedback form and all the -subsystems are not required to be input-to-state stable. Since the system states are unmeasurable and the output can only be measured at the sampling instants, an observer is designed to estimate the state. By adopting the multiple Lyapunov function method and the backstepping technique, a virtual controller is constructed, then a sampled-data controller is obtained by discretizing the designed virtual controller. With appropriate choice of a switching law and an allowable sampling period, it is proved that the designed sampled-data controller renders the corresponding closed-loop system to be globally practically stable. Finally, two examples are presented to illustrate effectiveness of the proposed methods.

Adaptive Fuzzy Prescribed Performance Control for MIMO Stochastic Nonlinear Systems

This paper investigates the adaptive fuzzy output feedback prescribed performance control (PPC) problem for multiple-input and multiple-output (MIMO) stochastic nonlinear systems in the nonstrict-feedback form. The study of MIMO nonlinear stochastic systems is assumed to have non-structural uncertainty, unknown control directions, and unknown dead zones. The fuzzy logic systems are adopted to approximate the unknown nonlinear functions, and a state observer is designed to estimate the unmeasured states. By combining backstepping recursive design principle with PPC theory, an observer-based adaptive fuzzy prescribed performance tracking control method is presented. In order to overcome the problem of unknown control directions in nonlinear stochastic systems, the Nussbaum gain function is introduced into adaptive fuzzy control design algorithm. The stability is proven based on the Lyapunov stability theory, which demonstrated that all the signals of the closed-loop systems are semi-globally uniformly ultimately bounded (SGUUB) in probability and the tracking errors remain a small neighborhood of the origin within the prescribed performance boundeds. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed approach.

Adaptive Neural Networks Decentralized FTC Design for Nonstrict-Feedback Nonlinear Interconnected Large-Scale Systems Against Actuator Faults.

The problem of active fault-tolerant control (FTC) is investigated for the large-scale nonlinear systems in nonstrict-feedback form. The nonstrict-feedback nonlinear systems considered in this paper consist of unstructured uncertainties, unmeasured states, unknown interconnected terms, and actuator faults (e.g., bias fault and gain fault). A state observer is designed to solve the unmeasurable state problem. Neural networks (NNs) are used to identify the unknown lumped nonlinear functions so that the problems of unstructured uncertainties and unknown interconnected terms can be solved. By combining the adaptive backstepping design principle with the combination Nussbaum gain function property, a novel NN adaptive output-feedback FTC approach is developed. The proposed FTC controller can guarantee that all signals in all subsystems are bounded, and the tracking errors for each subsystem converge to a small neighborhood of zero. Finally, numerical results of practical examples are presented to further demonstrate the effectiveness of the proposed control strategy.The problem of active fault-tolerant control (FTC) is investigated for the large-scale nonlinear systems in nonstrict-feedback form. The nonstrict-feedback nonlinear systems considered in this paper consist of unstructured uncertainties, unmeasured states, unknown interconnected terms, and actuator faults (e.g., bias fault and gain fault). A state observer is designed to solve the unmeasurable state problem. Neural networks (NNs) are used to identify the unknown lumped nonlinear functions so that the problems of unstructured uncertainties and unknown interconnected terms can be solved. By combining the adaptive backstepping design principle with the combination Nussbaum gain function property, a novel NN adaptive output-feedback FTC approach is developed. The proposed FTC controller can guarantee that all signals in all subsystems are bounded, and the tracking errors for each subsystem converge to a small neighborhood of zero. Finally, numerical results of practical examples are presented to further demonstrate the effectiveness of the proposed control strategy.

Adaptive neural control of switched nonstrict-feedback nonlinear systems with multiple time-varying delays

This paper focuses on the problem of adaptive neural tracking control for a class of uncertain switched nonlinear time-varying delay systems in nonstrict-feedback form with arbitrary switchings. Radial basis function neural networks are used to model the unknown redefined continuous functions derived from Young’s inequalities. By combining bounding functions’ monotonously increasing property and variable separation technique, the uncertain system functions with nonstrict-feedback structure are dealt with such that iterative adaptive backstepping approach can be carried out. A newly developed Lyapunov–Krasovskii functional is utilized to compensate for the uncertainties of multiple time-varying delays, which makes the delay nonlinearities free from any assumptions. By introducing novel continuous functions, the problem of circular construction of controller is overcome deduced from employing one common tuning law. It is proved that the tracking error of adaptive neural control systems is semi-globally uniformly ultimately bounded with common Lyapunov function method. Finally, a simulation example is presented to show the effectiveness of the suggested control scheme.

Finite-Time Adaptive Control for a Class of Nonlinear Systems With Nonstrict Feedback Structure.

This paper focuses on finite-time adaptive neural tracking control for nonlinear systems in nonstrict feedback form. A semiglobal finite-time practical stability criterion is first proposed. Correspondingly, the finite-time adaptive neural control strategy is given by using this criterion. Unlike the existing results on adaptive neural/fuzzy control, the proposed adaptive neural controller guarantees that the tracking error converges to a sufficiently small domain around the origin in finite time, and other closed-loop signals are bounded. At last, two examples are used to test the validity of our results.