A model reference adaptive control without strictly positive real condition (Q2745592)

The problem of model reference adaptive control is considered for a stochastic system with unmodeled dynamics \(\eta_n: A(z)y_n= B(z)u_n+ C(z)w_n+ \eta_{n-1}\), \(n\geq 1\), which is assumed to be dominated by \(|\eta_n|\leq\varepsilon \sum^n_{i=0} a^{n-i}(|y_i|+|u_i |+|w_i|+1)\), with \(a\in(0,1)\), \(\varepsilon\geq 0\), where \(A(z)\), \(B(z)\), \(C(z)\) are polynomials in backward shift operator, while \(y_i\), \(u_i\) and \(w_i\) denote the system output, input, and random disturbance sequences, respectively. The design method proposed for the adaptive controller relies on bounded external excitation and randomly varying truncation techniques. The strictly positive real condition used by other papers is relaxed to the stability of a polynomial. The closed-loop system controlled by the resulting model reference adaptive law is globally stable. The error for the parameter estimation in the modeled part of the considered system is of order \(\varepsilon\).