Optimal Mixed-Norm Control Synthesis for Discrete-Time Linear Systems

摘要

A mixed-norm approach to control synthesis for discrete time linear systems isdeveloped. Specifically, the problem of minimizing the H2 norm of a transfer function, subject to a combination of l1 and/or H-infinity norm constraints on dissimilar but related transfer functions is considered. The uniqueness of the optimal solution is shown, and numerical methods for approximating the optimal solution to within arbitrary accuracy are developed. These methods generally result in high order compensators which can not be implemented in most practical applications. In response to this, a numerical method is developed which solves for suboptimal solutions of a fixed, specifiable order. The method is packaged as a toolbox for the popular MATLAB software program. Several examples are developed which demonstrate potential applications for the mixed-norm method. (AN).