Direct Type Of The Discrete-time System, The Indirect Model Reference Adaptive Control, Robust Mixed

Discrete-time direct model reference adaptive control and Robust hybrid indirect model reference adaptive control are considered in the paper, which is composed of the following two parts.1. The design and analysis of the discrete-time direct model reference adaptive control with the normalized adaptive law.Consider the following discrete-time LTI systemR_p(z)[y](t) = k_pZ_p(z)[u](t), t = {0,1,2... },where u(t),y(t) ∈ R are the input and output, respectively, Rp(z) = zⁿ +a_n-1z^n-1+...+a₁z + a₀, Z_p(z) = z^m + b_m-1z^m-1+...+b₁z + b₀ with k_p, a_iand b_j(i = 0,1, ... ,n- 1, j = 0,1,... ,m - 1) being unknown constant parameters. The reference model is chosen asy_m(t) = W_n(z)[r](t) (?) 1/P_m(z)[r](t),where r is the reference input which is assumed to be a uniformly bounded. The objective of MRAC is to find an output feedback control signal u(t) for the plant such that all the signals in the closed-loop plant are bounded and the tracking error e(t) (?) y(t) - y_m(t) â†' 0 as t â†' ∞. To design and analyze the MRAC scheme, the assumptions of the system and the reference model are needed in the first chapter.In this part, For a class of discrete-time systems, by reproving the discrete-time conclusions on the L_p and L_2δ relationship properties between the input and the output, and the swapping lemmas I and II, the stability and convergence properties of the discrete-time MRAC scheme are analyzed rigorously in a systematic fashion as in the continuous-time case.2. The design and analysis of the robust hybrid indirect model reference adaptive control.Consider the following LTI system with the unmodeled dynamic and input disturbanceyp{t) = Gp{s){\ + μAm(s)){up{t) + du(t)),where Gp(s) — Zp(s)/Rp(s) is the modeled part of the plant with Rp(s) = sn + IXTo aiS*, Zp(s) = kpZp(s) = Y?=objSj, bm = kp, and a,- and bj being unknown parameters. Am(s) is a unknown multiplicative uncertainty, /U > 0 is a parameter indicting the magnitude of Am(s), du is a bounded input disturbance. Control objective is to design up such that all the signals in the closed-loop plant are all uniformly bounded and the output yp tracks the following reference model output ym as close as possibleym(t) = Wm(s)r(t) = *g^for any reference signal r(t), where r(t) and r(t) are uniformly bounded. To meet the control objective, To design and analyze the MRAC scheme, the assumptions of the system, the reference model and the unmodel dynamic are needed in the second chapter.In this part, for general plants with unmodeled dynamics, input disturbance and any relative degree, the problem of robust hybrid indirect model reference adaptive control is considered. By establishing the relationship properties among discrete parameter estimates of the plant and controller and their interpolations, and reducing the normalized signal from the suitable filter polynomial chosen, stability and tracking performance of the closed-loop plant are analyzed rigorously.