Two Types Of Complex Systems, Adaptive Control Problem

This thesis mainly studies adaptive control problems for two kinds of systems: 1. Robust direct model reference adaptive control for MIMO systems with relative degree two; 2. Decentralized adaptive output feedback control for time-varying interconnected systems. It is composed of the following two parts.1. The design of the robust direct model reference adaptive control with relative degree twoConsider the following LTI system with input disturbance:y(t) = G_p(s)u + d,where G_p(s) is the transfer matrix of the system and it has uniform relative degree 2, that is, lim_{sâ†'∞}s²G_p(s)=K_p,the nonsingular matrix K_p is referred to as the HFG matrix, and d is a bounded disturbance.The control objective is to design an output feedback control u such that all the signals in the closed-loop system are all uniformly bounded and the output y can track the output yM of the following reference model as close as possibleyM(t)=W_m(s)r(t),where r(t) and r(t) are uniformly bounded. To meet the control objective, the assumptions of the system and the reference model are given in the second chapter.In this part, for the general system with input disturbance and relative degree 2, the problem of robust direct model reference adaptive control is considered, and the stability and tracking performance of the closed-loop system are analyzed strictly.2. Decentralized adaptive output feedback control for time-varying interconnected systemsConsider the following interconnected system consisting of N subsystems, and the ith subsystem is modelled by where u_i(t). y_i(t)∈R are the input and the output of the ith subsystem, respectively,f_ij^'(t,y_j)∈R^n_i andâ–³_ij(s)y_j(i≠j)denote the static interconnections and the dynamic interconnections respectively from the j subsystem to the i subsystem,â–³_ii (s) is the unmodelleddynamic in the i subsystem, andμ_ij andμ_ii (i, j=1,…, N) are positive scalars specifying the magnitudes of dynamic interconnections and unmodelled dynamics,ω_i(t)∈R^n_i denotesthe additive disturbances of the ith subsystem. The control objective is to design a decentralized adaptive output feedback controller such that all the signals in the closed-loop system are bounded and the output y_i converges to zero.In this part, by introducing input filters and a series of coordinate changes, a closedloop system is obtained. Based on the system, a design scheme of decentralized adaptive output feedback controller is given. It is proved that when the variation rates of time-varying parameters belong to L₁∩L_∞,disturbances belong to L₂∩L_∞and the magnitude of theunmodeled dynamics is changing in some range, all the signals in the closed-loop system are bounded, and the output of each subsystem converges to zero. The effectiveness of the control scheme is demonstrated by a simulation example.