Two Types Of System Model Reference Adaptive Control Problem Research

Improved continuous-time direct robust model reference adaptive control with switched adaptive law and discrete-time indirect model reference adaptive control are considered in the paper, which is composed of the following two parts.1. Improved continuous-time direct robust model reference adaptive control with switched adaptive law.Consider the following continuous-time LTI systemwhere u_p(t), y_p(t)∈R are the input and output of plant, respectively, highfrequency gain k_p is known, R_p(s)＝sⁿ+a_n-1 s^n-1 +…a₁ s+a₀, Z_p(s) = s^m +b^m-1s^m-1+…+b₁s+b₀ with a_i and b_j (i = 0,1,…,n—1, j = 0,1,…,m—1)being unknown constant parameters, d)u is a bounded input disturbance. The reference model is chosen aswhere y_m is the output of the reference model, r is the reference input which is assumed to be uniformly bounded.The objective of RMRAC is to find an output feedback control signal u(t) for the plant such that all the signals in the closed-loop plant are uniformly bounded and the plant output y_p(t) tracks y_m(t) as close as possible, and if d_u = 0, the tracking error e(t) (?) y(t)—y_m(t)�'0 as t�'∞.To design and analyze the RMRAC scheme, the assumptions of the system and the reference model are needed in the second chapter.2. The design and analysis of discrete-time indirect model reference adaptive control with normalized adaptive law: a systematic approach. Consider the following discrete-time LTI system:where u,y∈R are the input and output of plant, respectively, t∈{0,1, 2…},with b_m^* = k_p, a_i^* and b_j^* being unknown constant parameters. The symbol z is used to denote the z-transform variable or time advance operator with the definition of z[x](t) = x(t+1), i.e., z^-1 is the delay operate z^<sup>-1[x](t) = x(t—1).Control objective is to develop an discrete-time indirect adaptive control scheme by combining a control signal u(t) with an adaptive estimator for unknown parameters of the plant (3.2.1) such that all the signals in the closed-loop plant are uniformly bounded and for the following given reference model output y_m(t), the tracking error e(t)(?) y(t)—y_m(t)�'0 as t�'∞. The reference model is chosen aswhere reference input r(t) is uniformly bounded.To design and analyze the indirect MRAC scheme, the assumptions of the system and the reference model are needed in the third chapter.In this part, for discrete-time indirect model reference adaptive control scheme , as in the continuous-time case, by proving the necessary key lemma, such as the property lemma of normalized adaptive law, the property lemma of controller parameters and the lemma of fictitious normalized signal, a systematic analysis approach to the discrete indirect MRAC scheme is developed rigorously.