Robust Adaptive Control Of Complex Systems

This paper mainly deals with two theoretical problems of robust adaptive control. It is composed of two parts. . A Robust Adaptive Controller Based on Backstepping Technique Consider the following SISO plantwhererepresents the reduced-order plant model. y(s), m(.s) and d(.s) are the un-modeled dynamics of the system, du and dy arc input, and output disturbances, and 1 0 is a parameter.The control objective is to design an adaptive control law based on back-stopping technique such that all the signals are uniformly bounded, and the plant output tracks as close as possible a reference signal yr(t).We give the following assumptions for the plant:(P1) a0, ..., an-1, b0, ... , bm-1 are unknowm costants, and the high-frequency gain bm 0 is known.(P2) G(.s) is minimum phase, i.e. Z(s) is Hurwitz.(P3) The relative degree = n - m, and an upper bound for the order n of G(s), are known, > 0.(P4) s !/(s), d(s), m(s) are strictly proper transfer function, and is analytic in Re[s] - for sonic > 0. c > 0 represents arbitrary finite constant}.The reference signal yr(t) satisfies the following assumption:(Rl) yr(t), and its first p dcrivates are known and bounded, and yr() (t) ispiecewise continuous.In this part, for a more general kind of systems, we give the design method of a robust adaptive controller based on backstepping technique, and analyxe stability and performance of the closed-loop system. . Robust Model Reference Adaptive Control Using Kp = LDU Factorization for Multivariable SystemsConsider the following multivariable plantwhere u Rn, y Rn, G(.s) Rm m is the modeled part of the plant., m(s) is an unknown multiplicative perturbation matrix, d is a bounded disturbance, 0 is a parameter.Control objective is to design a control law so that all signals in the closed-loop plant are bounded and the tracking error e(t) = y(t) - yM(t) is small enough, whereyM = WM(s)r,where r Rm is a pieccwise continuous uniformly bounded signal, and r L ,.For the plant , we need the following assumptions:(Al) The transmission zeros of G(.s) have negative real parts, and every element of G-1(.s) is analytic in Re[s] - , > 0 is some constant.(A2) G(s) is strictly proper, has full rank and its modified left, interart.or matrix m(s) whose definition can be found in is diagonal and known.(A3) The observability index v of G(s) is known.(A4) The signs of leading principal minors of high frequency gain matrix Kp = lirn m(s)G(s) are known.(A5) rn(s) is proper, and every element, is analytic in Re[s] - for the above . For d, there exists known constant do such that |d| d0.For the reference model , we need assumptions:(Ml) All poles and zeros of WM(s) are stable, and every element is analytic in Re[s] .(M2) The zero structure at infinity of WM(S) is the same as that of G(.s), i.e., lim m(s)WM(s) is finite and nonsingular. Without loss of generality, we chooseIn this part,the problem on robust model reference adaptive control using high frequency gain Kp = LDU factorization for multivariable systems is studied. We give rigorous performance analysis of adaptive systems.