Multivariable Robust Direct Model Reference Adaptive Control

Multivariable robust direct model reference adaptive control using high-frequency gain matrix Kp=L2D2S2 factorization and Kp=S1D1U1 factorization are considered in this paper. The paper is mainly composed of the following two parts:1. The second chapter investigates the problem of multivariable robust direct model reference adaptive control using Kp=L2D2S2 factorizationConsider the following multivariable system y(t)=G(s)(I+μ△(s))(u(t)+d(t)) where y(t),u(t)∈Rmare output and input, G(s)=(gij(s))∈Rm×m[s], the parameters of gij(s)are considered to be unknown, s denotes the differentiation, s(x)=x,△(s)∈Rm×m[s]is an unknown multiplicative uncertainty, d(t)∈Rm is an unknown bounded disturbance,μ>0 is a parameter indicating the magnitude of△(s).Using high-frequency gain matrix Kp=L2D2S2 factorization, the part generalizes the results of ideal multivariable system to the system which contains unknown multiplicative uncertainty and bounded disturbance. The multivariable robust direct model reference adap-tive control(RMRAC)scheme is considered and the stability and robustness are proofed rig-orously.2. The third chapter investigates the problem of multivariable robust direct model ref-erence adaptive control using Kp=SiD1U1 factorizationConsider the following multivariable system (I+μ1△1(s))y(t)= G(s)(I+μ2△2(s))(u(t)+d(t)) where y(t),u(t)∈Rmare output and input, G(s)=(gij(s))∈Rmxm[s], the parameters of gij(s) are considered to be unknown, s denotes the differentiation, s(x)=x,△1(s),△2(s)∈Rm×m[s]are unknown multiplicative uncertainties, d(t)∈Rm is an unknown bounded dis-turbance,μ1,μ2> 0 are parameters indicating the magnitude of△1(s),△2(s) respectively.Using high-frequency gain matrix Kp=S1D1U1 factorization, the part generalizes the results of ideal multivariable system to the system which contains not only input and output unknown multiplicative uncertainties, but also bounded disturbance. The multivariable ro-bust direct model reference adaptive control(RMRAC)scheme is considered and the stability and robustness are proofed rigorously.