Controller reduction in l1 optimal control

Outlines an approach for the computation of a suitable low order controller given a linear discrete-time multi-input multi-output control system with a high order controller. This step is of significant importance in the case of l₁ optimal control system design based on linear programming with its inherent problem of inflating controller order. Since the main focus during controller reduction is to maintain the performance of the closed loop system this task is quite different from the general order reduction problem and thus requires special methods. The main contribution of the paper is the presentation of a controller reduction method which is based on linear programming. In this way, the l₁ optimal control system design is augmented by a second phase-similar to the famous simplex algorithm for solving linear programs-and avoids severe difficulties during the controller implementation. The efficiency of the proposed method is demonstrated by an example.