Adaptive control of linear unstable and nonminimum-phase plants
A discrete-time single-input single-output adaptive control problem which includes both unstable and nonminimum phase plants is considered. The plant is under the action of a disturbance bounded by \(\delta\). The control \(u_ n\) is determined by the minimax principle. That is, \(u_ n\) is determined so as to minimize a criterion function maximized by an unknown parameter vector L in the estimate \(\Omega_ L^{(n)}\) and also by an unknown disturbance in the prescribed set \(\Omega_{\lambda}\). The estimate \(\Omega_ L^{(n)}\) is successively narrowed by an identification process. That is \(\Omega_ L^{(n+1)}={\tilde \Omega}_ L^{(n+1)}\cap \Omega_ L^{(n)},\) where \({\tilde \Omega}{}_ L^{(n+1)}\) is determined by the inequality based on the transition from \(x_ n\) to \(x_{n+1}\).
discrete-time single-input single-output adaptive control problem
scientific article; zbMATH DE number 3914205