Robust Adaptive Control Of Complex Systems Research

This paper mainly deals with two theoretical problems of robust adaptive control. It is composed of two parts.一. Robust Direct Model Reference Adaptive Control for Relative Degree n* = 3 System with Unmodeled DynamicsConsider the following SISO plantwhere are the plant input and output, respectively, , parameters ai and bj(i = 0,...,n -1, j = 0, ...,m -1) are unknown constants, k(s)(k = 1,2) are the unmodeled dynamics of the system, (k = 1,2) are parameters.The control objective is to design a robust direct model reference adaptive control law up with unnormalized adaptive law such that all signals in the closed-loop plant are bounded and the tracking error e1(t) yP(t)-ym(t) is small enough, wherewhere ym,r R1, r(t) is a piecewise continuous uniformly bounded signal.We give the following assumptions for the plant:(P1) Zp(s) is Hurwitz polynomial;(P2) The relative degree of Gp(s) is n* = n - m = 3;(P3) The sign of the plant high-frequency gain Kp is unknown and there exist a constant K > 0 such that |KP| > K.For the reference model , we need assumptions:(M1) Zm(s),Rm(s) are monic Hurwitz polynomials of degree qm,pm respectively ,where pm < n;(M2) The relative degree of the reference model equals to n* = pm - qm= 3;(M3) The reference input In this part, for a kind of systems with unmodeled dynamics and the relative degree n* = 3, we give the design method of a robust direct model reference adaptive controller with unnormalized adaptive law, and analyze stability and performance of the closed-loop system.二. Adaptive Backstepping Control of Decentralized Plants with Time-varying ParametersConsider the following large-scale system consisting of N interconnected sub-systems,and the ith subsystem is modelled bywhere are the local states,output and input, respectively; are time-varying matrices,Coi is constant matrice; and denote,respectively,the static interactions and the dynamic interactions from the jth subsystem to the ith subsystem; ii(s) is the unmodeled dynamics in the ith subsystem;and uij> 0 are parameters.Control objective is to design a local adaptive controller for each subsystem such that the overall interconnected system is stable and all the outputs yi is sufficiently small asymptotically.For the plant , we need the following assumptions:Asumption 1(1) The plant order ni and its relative degree are known;(2) The sign of the plant high-frequency gain bmii(t) is knowm and there exist a constant > 0 such that (3) The polynomial is uniformly Hur-witz, i.e. all zeros of Bit(s) satisfy the equality: Re(zij(t)) <-6, Vt >0 for some constant 6 >0. Asumption 2(1) Time functions ai(t) and bj(t) are difFerentiable and bounded, and there derivatives are both piecewise continuous and bounded, i.e. there exist constants such that (2) Upper bound and known,where unknown parameter vectors.Asumption 3For the nonlinear interactions fij(t,yj), we have where > 0.Asumption 4 are stable and strictly proper with unity high- frequency gains.In this part, for a large-scale system consisting of N interconnected subsystems with arbitrary degree, we continue to study the robust adaptive control problem and give rigorous performance analysis of the closed-loop system.