Class Of First-order Nonlinear Systems Research Articles

Exponential Stability for Adaptive Control of a Class of First-Order Nonlinear Systems

In adaptive control it is typically proven that a weak asymptotic form of stability holds; furthermore, at best it is proven that a bounded noise yields a bounded state. Recently, however, it has been proven in a variety of scenarios that it is possible to carry out adaptive control for a linear-time invariant (LTI) discrete-time plant so that the closed-loop system enjoys exponential stability, a bounded gain on the noise, as well as a convolution bound on the effect of the exogenous inputs; the key idea is to carry out parameter estimation by using the ideal projection algorithm in conjunction with restricting the parameter estimates to a convex set. In this paper we extend the approach to a class of first-order nonlinear systems.

Nonlinear adaptive learning control for unknown time‐varying parameters and unknown time‐varying delays

AbstractA new adaptive learning control approach is proposed for a class of first‐order nonlinear systems with two unknown time‐varying parameters and an unknown time‐varying delay. By reconstructing the system equation, all unknown time‐varying terms, including the time‐varying delay, are combined into an unknown periodic time‐varying vector, which is estimated by a periodic adaptive mechanism. By constructing a Lyapunov–Krasovskii‐like composite energy function (CEF), we prove the boundedness of all signals and the convergence of the tracking error. The results are extended to two classes of high‐order nonlinear systems with mixed parameters. Three simulation examples are provided to illustrate the effectiveness of the control algorithms proposed in this paper.Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Robust control of a class of uncertain first-order systems with least prior knowledge

In this work we deal with robust control of a class of first-order nonlinear systems which contain uncertainties. To cope with the uncertainties, an observer-based controller is proposed, and the uniform boundedness of all closed-loop signals and semiglobal practical convergence of the system state are guaranteed. In contrast with some previous attempts to relax the a priori knowledge on uncertainties bounds by using discontinuous control law, we propose a dynamic compensator which leads to continuous control laws. The applicability of the control scheme to regulation of temperature in stirred tanks and one-point control in distillation is shown by numerical simulations.

Adaptive control of first-order nonlinear systems with reduced knowledge of the plant parameters

This paper presents an adaptive control strategy for a class of first-order nonlinear systems of the form x/spl dot/=/spl theta//sub 1/*/sup T/f(x)+/spl theta//sub 2/*/sup T/g(x), where g(x) is a smooth function, whereas f(x) satisfies sectoricity conditions. /spl theta//sub 1/* and /spl theta//sub 2/* are constant parameter vectors. It is assumed that the system remains controllable for all values of x, but the sign of /spl theta//sub 2/*/sup T/g(x)(x) is unknown. The proposed adaptive scheme extends ideas previously presented the authors (1992) where the term premultiplying the input was supposed to be constant. The standard least-squares estimates of /spl theta//sub 2/* are modified using a hysteresis type switching algorithm that enables us to conclude on existence, uniqueness, boundedness and convergence of the solutions of the adaptive closed-loop system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

First-order nonlinear systems governed by generalised Riccati partial-differential equation

The letter presents a method of converting a class of first-order nonlinear systems, represented by Riccati type of partial-differential equations, into equivalent linear second-order systems. The familiar Riccati equations and the linear equivalent second-order equation form a particular case of this study.