Adaptive Output Feedback Tracking Control for a Class of Uncertain Nonlinear Systems Using Neural Networks

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.

ABSTRACTThis paper is concerned with the global practical tracking via adaptive output feedback for a class of uncertain nonlinear systems. The system under investigation possesses function control coefficients, the polynomial-of-output growth rate and serious unknowns in the system nonlinearities and the reference signal, and hence is essentially different from those in the closely related literature. To solve the problem, a high-gain observer is introduced to reconstruct the unmeasured system states. The involved high gain is the multiplication of two dynamic gains: one is to compensate the polynomial-of-output in the system growth rate, and the other one is to overcome the serious unknowns in the system and reference signal and the extra system nonlinearities in function control coefficients. Based on the high-gain observer, an adaptive output-feedback controller is successfully designed to guarantee that, for any initial condition of the system, all signals of the closed-loop system are bounded, and the tracking error will be prescribed sufficiently small after a finite time. A numerical example demonstrates the effectiveness of the proposed method.

Adaptive fuzzy tracking control for a class of uncertain nonaffine nonlinear systems with dead-zone inputs

This paper deals with the global output feedback tracking control problem for a class of switched nonlinear systems involving unknown parameters and unmeasured states multiplied by output nonlinearities. The switching information is assumed to be unobservable. To approach this purpose, a modified high-gain observer is introduced, and then an adaptive output feedback controller is constructed by adopting the adaptive backstepping technique. It is shown that, under arbitrary switching the proposed controller can guarantee all signals of the closed-loop system are globally uniformly bounded and the tracking error converges to a residual set that can be made arbitrarily small by properly selecting the design parameters. Simulation results are presented to verify the effectiveness of the proposed approach.

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.

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.

This paper focuses on the problem of adaptive output feedback tracking control for a class of nonstrict-feedback nonlinear systems with unknown control coefficients and quantized input. The difficulty from the unknown control direction is solved by using the linear state transformation and the Nussbaum gain function(NGF) approach. Based on the combination of input-driven observer, backstepping technique, neural network(NN) parametrization and variable separation method, a novel adaptive output feedback quantized control scheme involving only one adaptive parameter is developed for such systems. The designed quantized controller ensures that all signals of closed-loop systems are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error converges to an adjustable neighborhood of the origin. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed control design.

This paper mainly focuses on output feedback practical tracking controller design for stochastic nonlinear systems with polynomial function growth conditions. Mostly, there are some studies on output feedback tracking control problem for general nonlinear systems with parametric certainty in existing achievements. Moreover, we extend it to stochastic nonlinear systems with parametric uncertainty and system nonlinear terms are assumed to satisfy polynomial function growth conditions which are more relaxed than linear growth conditions or power growth conditions. Due to the presence of unknown parametric uncertainty, an output feedback practical tracking controller with dynamically updated gains is constructed explicitly so that all the states of the closed-loop systems are globally bounded and the tracking error belongs to arbitrarily small interval after some positive finite time. An example illustrates the efficiency of the theoretical results.

This paper focuses on the problem of adaptive output feedback tracking control for a class of non-strict-feedback nonlinear systems with unknown control coefficients. By employing a linear state transformation, the original system is transformed to a new system for which control design becomes feasible. Then, after the introduction of a simple input-driven observer, an adaptive output feedback controller which contains only one parameter is developed for such systems by using backstepping technique and variable separation method. The designed controller ensures that all the signals in the closed-loop systems are Semi-globally Uniformly Ultimately Bounded (SGUUB).

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.

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

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 article studies the adaptive output feedback control problem of a class of uncertain nonlinear systems with unknown time delays. The systems considered are dominated by a triangular system without zero dynamics satisfying linear growth in the unmeasurable states. The novelty of this article is that a universal-type adaptive output feedback controller is presented to time-delay systems, which can globally regulate all the states of the uncertain systems without knowing the growth rate. An illustrative example is provided to show the applicability of the developed control strategy.

This brief deals with the problem of semi-global stabilization by output feedback for a class of uncertain nonlinear systems. Due to the presence of mismatched uncertainties and the lack of triangularity condition, the systems under consideration are not uniformly completely observable. In addition, the uncertain nonlinear dynamics of the systems are higher order, rather than linearly growing, in the unmeasurable states. All these make the systems not semi-globally stabilizable by the existing output feedback design schemes. In this brief, by extending the feedback domination design techniques proposed by Qian and Lin, a systematic design scheme is developed to construct linear output feedback controllers that semi-globally stabilize a general class of uncertain nonlinear systems under less restrictive conditions.

In this paper the exponential tracking problem for a class of single-input nonlinear uncertain systems expressed in canonical Brunowsky form, with nonaffine dependence on the control, is addressed and solved by a second-order sliding-mode control methodology. The presence of unmodelled first-order actuators is considered in the design procedure, and the proposed controller provides for a global domain of attraction and counteracts the typical transient peaking of the state trajectory. Computer simulations confirm the feasibility of the proposed approach.