Systems In Strict-feedback Form Research Articles

Adaptive neural control for a class of time‐delay systems in the presence of backlash or dead‐zone non‐linearity

This study addresses the adaptive tracking control problem for a class of time-delay systems in strict-feedback form with unknown control gains and uncertain actuator non-linearity. The actuator non-linearity can be either backlash or dead zone, and the proposed approach does not require the knowledge of the bounds of non-linearity parameters. By applying an appropriate Lyapunov–Krasovskii functional and utilising the property of the well-defined trigonometric functions, the problems of time delay and controller singularity are avoided. The feasibility of using a static neural network to attenuate the effect of actuator non-linearity is proved with the aid of intermediate value theorem. Furthermore, it is proved that all closed-loop signals are bounded and the tracking error converges to a small residual set asymptotically. Two simulation examples are provided to demonstrate the effectiveness of the designed method.

Dynamic surface error constrained adaptive fuzzy output-feedback control of uncertain nonlinear systems with unmodeled dynamics

In this paper, an adaptive fuzzy output-feedback dynamic surface control (DSC) design with prescribed performance is investigated for a class of uncertain nonlinear systems in strict-feedback form. The considered nonlinear systems contain unknown nonlinear functions, unmodeled dynamics and immeasurable states. The fuzzy logic systems are used to model the unknown nonlinear system, and a fuzzy state observer is designed to estimate the immeasurable states. By transforming the errors into new virtual error variables, and based on DSC backstepping design technique and changing supply function, a new robust adaptive fuzzy output feedback control scheme is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed–loop system are bounded, and the dynamic surface errors are confined within the prescribed bounds for all times. Two simulation examples are provided to show the effectiveness of the proposed control approach.

Fuzzy Adaptive Actuator Failure Compensation Control of Uncertain Stochastic Nonlinear Systems With Unmodeled Dynamics

This paper investigates fuzzy adaptive actuator failure compensation control for a class of uncertain stochastic nonlinear systems in strict-feedback form. These stochastic nonlinear systems contain the actuator faults of both loss of effectiveness and lock-in-place, unmodeled dynamics, and without direct measurements of state variables. With the help of fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is established to estimate the unmeasured states. By introducing the dynamical signal and the changing supply function technique design into the backstepping control design, a robust adaptive fuzzy fault-tolerant control scheme is developed. It is proved that the proposed control approach can guarantee that all the signals of the closed-loop system are bounded in probability in the presence of the actuator failures and the unmodeled dynamics. Simulation results are provided to show the effectiveness of the control approach.

Robust adaptive control of switched non-linear systems in strict feedback form with unknown time delay

Robust adaptive control of switched non-linear systems in strict feedback form with unknown time delay

Composite Neural Dynamic Surface Control of a Class of Uncertain Nonlinear Systems in Strict-Feedback Form

This paper studies the composite adaptive tracking control for a class of uncertain nonlinear systems in strict-feedback form. Dynamic surface control technique is incorporated into radial-basis-function neural networks (NNs)-based control framework to eliminate the problem of explosion of complexity. To avoid the analytic computation, the command filter is employed to produce the command signals and their derivatives. Different from directly toward the asymptotic tracking, the accuracy of the identified neural models is taken into consideration. The prediction error between system state and serial-parallel estimation model is combined with compensated tracking error to construct the composite laws for NN weights updating. The uniformly ultimate boundedness stability is established using Lyapunov method. Simulation results are presented to demonstrate that the proposed method achieves smoother parameter adaption, better accuracy, and improved performance.

A Small-Gain Theorem for Switched Interconnected Nonlinear Systems and Its Applications

A small-gain theorem for switched interconnected nonlinear systems is set up which provides a tool for analyzing the behavior of switched systems. Also, a method exploiting an average dwell time and the small gain technique is proposed. Based on the small-gain theorem, this technical note investigates the problem of global stabilization of switched nonlinear systems in strict-feedback form whose all zero dynamics are input-to-state stable (ISS) or only some are ISS and others are not. A sufficient condition for the global stabilization problem under a class of switching signals with average dwell time is derived by constructing state-feedback controllers for subsystems. The result is also applied to a class of switched nonlinear network control systems.

Observer-Based Adaptive Decentralized Fuzzy Fault-Tolerant Control of Nonlinear Large-Scale Systems With Actuator Failures

This paper investigates the adaptive fuzzy decentralized fault-tolerant control (FTC) problem for a class of nonlinear large-scale systems in strict-feedback form. The considered nonlinear system contains the unknown nonlinear functions, i.e., unmeasured states and actuator faults, which are modeled as both loss of effectiveness and lock-in-place. With the help of fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive observer is designed to estimate the unmeasured states. By combining the backstepping technique with the nonlinear FTC theory, a novel adaptive fuzzy decentralized FTC scheme is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded, and the tracking errors between the system outputs and the reference signals converge to a small neighborhood of zero by appropriate choice of the design parameters. Simulation results are provided to show the effectiveness of the control approach.

Adaptive Backstepping Control for a Class of Uncertain Nonaffine Nonlinear Time-Varying Delay Systems with Unknown Dead-Zone Nonlinearity

An adaptive backstepping controller is constructed for a class of nonaffine nonlinear time-varying delay systems in strict feedback form with unknown dead zone and unknown control directions. To simplify controller design, nonaffine system is first transformed into an affine system by using mean value theorem and the unknown nonsymmetric dead-zone nonlinearity is treated as a combination of a linear term and a bounded disturbance-like term. Owing to the universal approximation property, fuzzy logic systems (FLSs) are employed to approximate the uncertain nonlinear part in controller design process. By introducing Nussbaum-type function, the a priori knowledge of the control gains signs is not required. By constructing appropriate Lyapunov-Krasovskii functionals, the effect of time-varying delay is compensated. Theoretically, it is proved that this scheme can guarantee that all signals in closed-loop system are semiglobally uniformly ultimately bounded (SUUB) and the tracking error converges to a small neighbourhood of the origin. Finally, the simulation results validate the effectiveness of the proposed scheme.

Adaptive fuzzy decentralised fault-tolerant control for nonlinear large-scale systems with actuator failures and unmodelled dynamics

This paper discusses the adaptive fuzzy decentralised fault-tolerant control (FTC) problem for a class of nonlinear large-scale systems in strict-feedback form. The systems under study contain the unknown nonlinearities, unmodelled dynamics, actuator faults and without the direct measurements of state variables. With the help of fuzzy logic systems identifying the unknown functions and a fuzzy adaptive observer is designed to estimate the unmeasured states. By using the backstepping design technique and the dynamic surface control approach and combining with the changing supply function technique, a fuzzy adaptive FTC scheme is developed. The main features of the proposed control approach are that it can guarantee the closed-loop system to be input–to-state practically stable, and also has the robustness to the unmodelled dynamics. Moreover, it can overcome the so-called problem of ‘explosion of complexity’ existing in the previous literature. Finally, simulation studies are provided to illustrate the effectiveness of the proposed approach.

Inverse optimal adaptive stochastic gain assignment for a class of nonlinear systems with Markovian jump

This paper deals with the inverse optimal adaptive stochastic gain assignment problem for a class of Markovian jump nonlinear systems with constant unknown parameters. The Wiener noises have bounded but unknown covariance. It is shown that a sufficient condition to solve this problem is the existence of a Lyapunov function for a corresponding auxiliary system. By employing backstepping technique and common Lyapunov function method, an adaptive control law is designed, which solves this problem for a class of Markovian jump nonlinear systems in strict-feedback form. A numerical example is given to illustrate the theoretical analysis result.

Global stabilization of switched stochastic nonlinear systems in strict-feedback form under arbitrary switchings

This paper is concerned with the problem of global stabilization in probability for a class of switched stochastic nonlinear systems under arbitrary switchings. The subsystems are assumed to be in strict-feedback form and driven by white noise. By introducing a common Lyapunov function, the common state feedback controller independent of switching signals is constructed based on the backstepping approach. It is proved that the zero solution of the closed-loop system is fourth-moment globally exponentially stable. Two examples are given to show the effectiveness of the proposed method.

Backstepping designs for the stabilisation of nonlinear sampled-data systems via approximate discrete-time model

The problems of backstepping, adaptive backstepping and reduced order observer based output feedback control of sampled-data nonlinear systems in strict feedback form are considered. Controller design methods based on the Euler approximate model are presented for these problems. The controllers are designed to compensate the effects of the discrepancy between the Euler approximate model and exact discrete time model, parameter estimation error in adaptive control and observer error in output feedback control, which behave as disturbance. It is shown that the obtained controllers semi-globally practically asymptotically stabilise the plant model under standard assumptions. Then numerical examples are given to illustrate the design methods.

Distributed adaptive containment control of uncertain nonlinear multi-agent systems in strict-feedback form

This paper presents a distributed containment control approach for uncertain nonlinear strict-feedback systems with multiple dynamic leaders under a directed graph topology where the leaders are neighbors of only a subset of the followers. The strict-feedback followers with nonparametric uncertainties are considered and the local adaptive dynamic surface controller for each follower is designed using only neighbors’ information to guarantee that all followers converge to the dynamic convex hull spanned by the dynamic leaders where the derivatives of leader signals are not available to implement controllers, i.e., the position information of leaders is only required. The function approximation technique using neural networks is employed to estimate nonlinear uncertainty terms derived from the controller design procedure for the followers. It is shown that the containment control errors converge to an adjustable neighborhood of the origin.

A sum of squares approach to backstepping controller synthesis for piecewise affine and polynomial systems

SUMMARY This paper develops a backstepping controller synthesis methodology for piecewise polynomial (PWP) systems in strict form. The main contribution of the paper is to formulate sufficient conditions for controller design for PWP systems in strict form as a sum of squares feasibility problem under the assumption that an initial control Lyapunov function exists to start the iterative backstepping procedure. This problem can then be translated into a convex SDP problem and solved by available software packages. The controller synthesis problem for PWP systems in strict feedback form is divided into two cases. The first case consists of the construction of a sum of squares polynomial control Lyapunov function for PWP systems with discontinuous vector fields. The second case addresses the construction of a PWP control Lyapunov function for PWP systems with continuous vector fields. One major advantage of the proposed method is the fact that it can handle systems with discontinuous vector fields and sliding modes. The new synthesis method is applied to several numerical examples. One of these examples offers the first convex optimization solution to piecewise affine (PWA) control of a benchmark circuit system addressed before in the literature using non-convex PWA control solutions. Copyright © 2013 John Wiley & Sons, Ltd.

Finite-time stabilization of stochastic nonlinear systems in strict-feedback form

In this paper, we investigate the problem of almost surely finite-time stabilization of a class of stochastic nonlinear systems. Based on the recently proposed almost surely finite-time stability theorem in Yin, Khoo, Man, and Yu (2011), we prove that, almost surely global finite-time stability of stochastic nonlinear systems in strict-feedback form can be guaranteed by a continuous control law. A systematic design algorithm is developed for the construction of the controller. Simulation results are given to illustrate the theoretical analysis.

Adaptive fuzzy control of uncertain stochastic nonlinear systems with unknown dead zone using small-gain approach

This paper considers the adaptive fuzzy robust control problem for a class of single-input and single-output (SISO) stochastic nonlinear systems in strict-feedback form. The systems under study possess unstructured uncertainties, unknown dead-zone, uncertain dynamics and unknown gain functions. In the controller design, fuzzy logic systems are adopted to approximate the unknown functions, and the uncertain nonlinear system is therefore transformed into an uncertain parameterized system with unmodeled dynamics. By combining the backstepping technique with the stochastic small-gain approach, a novel adaptive fuzzy robust control scheme is developed. It is shown that the proposed control approach can guarantee that the closed-loop system is input-state-practically stable (ISpS) in probability, and the output of the system converges to a small neighborhood of the origin by appropriately tuning several design parameters. Simulation results are provided to illustrate the effectiveness of the proposed control approach.

Adaptive disturbance rejection for strict-feedback switched nonlinear systems using multiple Lyapunov functions

SUMMARY This paper investigates the problem of global disturbance rejection for switched nonlinear systems in strict-feedback form with unknown exosystem where the solvability of the disturbance rejection problem for subsystems is not assumed. First, a sufficient condition for the solvability of the global disturbance rejection problem is given. As an extension of the classic concept of internal model for non-switched systems, a new concept of switched internal model is proposed. Second, in order to solve the problem in question, a constructive adaptive control methodology is established on the basis of the multiple Lyapunov functions method, backstepping, and the changing supply functions technique. Finally, an example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.

Fuzzy almost disturbance decoupling for MIMO nonlinear uncertain systems based on high-gainobserver

The problem of disturbance decoupling with internal stability is investigated for a class of multi-input–multi-output (MIMO) nonlinear systems in strict-feedback form. The considered nonlinear system contains unknown nonlinear uncertainties and unmeasured states. Fuzzy logic systems are first utilized to approximate the unknown nonlinear uncertainties, and then a high-gain state observer is established to estimate the unmeasured states. Based on the backstepping design approach and combining with dynamic surface control (DSC) technique, a new fuzzy adaptive output feedback control scheme is constructed. It is proved that the proposed control scheme can not only achieve internal stability of the closed-loop system, but also diminish the effect of the disturbance on output in the sense of L2 gain. In addition, since DSC is introduced into the backstepping design, the proposed control scheme can overcome the problem of “explosion of complexity” inherent in the traditional backstepping design. Simulation results and comparisons with the previous methods are included to indicate that the proposed adaptive fuzzy control approach has a satisfactory control performance.

Stability Analysis of Quantized Feedback Control System

This paper studies the feedback control problem of nonlinear systems in strict-feedback form with state quantizers, which are static and bounded by sectors. Through a newly developed and versatile Lyapunov function analyzing approach for networked and quantized control systems (NQCSs). The common aim is to demonstrate that a unified study of quantization and delay effects in an uncertain system is possible by merging the quantized control law. A new delays-independent stability criterion is derived in terms of linear matrix inequality (LMI) which can be easily solved. This paper describes a system for the stability analysis of the uncertain systems subject to quantization and time-delay. Moreover, a sufficient condition for the existence of a guaranteed cost controller for NCSs is also presented by a set of LMIs. Both theoretical analysis and numerical examples show that the results in this paper are generally less conservative than those in the quadratic framework.

Fuzzy adaptive fault-tolerant output feedback control of multi-input and multi-output non-linear systems in strict-feedback form

This study develops an adaptive fuzzy control method for accommodating actuator faults in a class of uncertain multi-input and multi-output non-linear systems in strict-feedback form and without the requirement of their states being available for controller design. The considered faults are modelled as both loss-of-effectiveness and lock-in-place (stuck at unknown place). With the help of fuzzy logic systems to approximate the unknown non-linear functions, a fuzzy adaptive observer is developed for estimating the unmeasured states. Combining backstepping technique with non-linear tolerant-fault control theory, a novel adaptive fuzzy fault-tolerant control approach is constructed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded, and also the tracking errors between the system outputs and the reference signals converge to a small neighbourhood of zero by appropriate choice of the design parameters. Simulation results are provided to show the effectiveness of the control approach.