Robust output feedback stabilization of nonlinear systems

This paper investigates the problem of robust output feedback stabilization of uncertain Hamiltonian systems with saturating actuator and input delay. The uncertainties are assumed to be time invariant and belong to convex bounded polytopic domain. By employing Lyapunov-Krasovskii functional method and Wirtinger's inequality, some sufficient conditions are derived for stabilization of nonlinear Hamiltonian systems under consideration. A delay-independent condition in terms of linear matrix inequalities for control of the Hamiltonian systems is established first. And further, an output feedback controller synthesis scheme under the multiple Lyapunov functional framework is proposed which guarantees the robust stability of the closed-loop system when control saturation and delay effectively occur. Finally, numerical results are given to demonstrate the effectiveness of the proposed methodology.

The problem of memoryless robust stabilization is discussed for a class of nonlinear uncertain systems with time-varying delay. The time-varying delay is assumed to unknown but known bound. The uncertainties are dependent on the delay states and have known bounds. No matching and Lipschitz's boundedness conditions are required. The continuous state feedback controller is proposed based on the Lyapunov direct methods such that the trajectories of the closed-loop nonlinear uncertain time-delay systems are uniformly and ultimately bounded on a compact set of which the diameter can be made arbitrarily large by choosing design parameters. The authors show that several previous results can be considered as a special cases. The effectiveness of the proposed approaches are demonstrated by the simulation results.

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.

In this paper, the problem of delay-dependent robust dynamic output feedback stabilization for a class of uncertain singular time-delay system is investigated. Based on the delay-dependent stability criterion for nominal singular time-delay systems and the concept of generalized quadratic stabilization, the sufficient conditions of the existence of the feedback controller are obtained, which ensure that the closed-loop systems are regular, impulse free and robustly asymptotically stable. Moreover, the expression for the desired robustly stabilizing controller is given by using the LMIs and the cone complementarity linearization iterative algorithm.

SummaryIn this paper, we aim at addressing the problem of global output feedback stabilization for a class of uncertain nonlinear systems with quantized input and output. The nonlinear functions of the system are assumed to satisfy high‐order growth condition on the unmeasurable states. Based on the homogeneous domination approach and sector bound approach, a homogeneous quantized controller computed from quantized output is constructed, and a guideline is derived to select the parameters of the quantizers. Further, it is proved that, with the proposed scheme, the closed‐loop system is globally asymptotically stable. Copyright © 2016 John Wiley & Sons, Ltd.

The robust output feedback stabilization problem for state-delayed systems with time-varying delays and saturating actuators is addressed here. The systems considered are continuous-time, with parametric uncertainties entering all the matrices in the system representation. A saturating control law is designed and a region of initial conditions is specified within which local asymptotic stability of the closed-loop system is ensured. The least conservative approach that employs the Lyapunov–Krasovskii functional is adopted to ensure stabilization. The designed controller is dependent on the time-delay and its rate of change. The controller is constructed in terms of the solution to a set of matrix inequalities.

Cascade control for a class of uncertain nonlinear systems: a backstepping approach

In this paper, a high-gain nonlinear observer based fault detection and diagnosis (FDD) approach is proposed for a general class of nonlinear uncertain systems with measured output probability density functions (PDFs). The objective of the presented FDD algorithm is to use the measured output probability density functions (PDFs) and the input of the system to construct a exponential observer-based residual generator such that the fault can be detected and diagnosed. The main result is given in a constructive manner by developing a novel nonlinear observer, without resort to any linearization. By a coordinates transformation, the design of the proposed observer does not necessitate the resolution of kind of linear matrix inequalities (LMIs) and its expression is explicitly given. The exponential convergence of the errors in the presence of parameters uncertainties is proved to guarantee the fastness of the proposed fault diagnosis scheme. Furthermore, the bound of the estimation errors in the presence the faults is minimized by appropriately choosing the parameters of the presented observer. Finally a simulation example is given to illustrate the efficiency of the proposed fault detection and diagnosis method.

ABSTRACTQuick and timely fault detection is of great importance in control systems reliability. Undetected faulty sensors could result in irreparable damages. Although fault detection and isolation (FDI) methods in control systems have received much attention in the last decade, these techniques have not been applied for some classes of nonlinear systems yet. This paper deals with the issues of sensor fault detection and isolation for a class of Lipschitz uncertain nonlinear system. By introducing a coordinate transformation matrix for states and output, the original system is first divided into two subsystems. The first subsystem is affected by uncertainty and disturbance. The second subsystem just has sensor faults. The nonlinear term is separated to linear and pure nonlinear parts. For fault detection, two sliding mode observers (SMO) are designed for the two subsystems. The stability condition is obtained based on the Lyapunov approach. The necessary matrices and parameters are obtained by solving the linear matrix inequality (LMI) problem. Furthermore, two sliding mode observers are designed for fault isolation. Finally, the effectiveness of the proposed approach is illustrated by simulation examples.

This correspondence addresses the problem of designing robust tracking control for a class of uncertain nonlinear MIMO second-order systems. An adaptive neural-network-based output feedback tracking controller is constructed such that all the states and signals involved are uniformly bounded and the tracking error is uniformly ultimately bounded. Only the output measurement is required for feedback. The implementation of the neural network basis functions depends only on the desired reference trajectory. Therefore, the intelligent adaptive output feedback controller developed here possesses the properties of computational simplicity and easy implementation. A simulation example of controlling mass-spring-damper mechanical systems is made to confirm the effectiveness and performance of the developed control scheme.

We consider single-input nonlinear systems with unknown unmodelled time-varying parameters or disturbances which are bounded. The main goal is to identify classes of uncertain systems for which the control exist and to provide design procedures. Assuming that the undisturbed nominal system (f,g) is partially state feedback linearizable, that a strict triangularity condition, a linear parametrization condition, and f/spl isin/G/sub r-1/ hold for the uncertain terms, and that some condition is satisfied in the transformed partially linear system, we design an adaptive regulating dynamic control. First, we identify classes of nonlinear uncertain systems and give a systematic procedure for the design of a robust regulation for the nonlinear systems.

Based on backstepping technique, an adaptive inverse control scheme is proposed for a class of uncertain nonlinear systems preceded by unknown hysteretic nonlinearities which are described by Krasnosel'skii-Pokrovkii (KP) model. The pseudo-inversion is introduced to compensate the hysteresis nonlinearities and the error caused by the hysteresis model and pseudo-inversion is estimated online by the adaptive controller. To avoid the possible chattering caused by the sign function, a smooth adaptive controller is designed. The proposed controller ensures the uniformly ultimate boundedness of the closed-loop system. Simulation results show the effectiveness of the proposed scheme.

Adaptive control of uncertain nonlinear systems using mixed backstepping and Lyapunov redesign techniques

Robust Output Feedback Design of Linear Discrete-Time Systems - LMI Approach

In this paper, an infinite horizon optimal robust guaranteed cost control scheme of a class of continuous-time uncertain nonlinear systems is established based on adaptive dynamic programming. The main idea lies in that the optimal robust guaranteed cost control problem can be transformed into an optimal control problem. Actually, the optimal cost function of the nominal system is nothing but the optimal guaranteed cost of the original uncertain system. A critic neural network is constructed to help solving the modified Hamilton-Jacobi-Bellman equation corresponding to the nominal system. Then, an additional stabilizing term is introduced to reinforce the updating process of the weight vector and reduce the requirement of an initial stabilizing control. An example is provided to illustrate the effectiveness of the present control approach.