Low sensitivity feedback control of non-linear discrete systems†

Abstract

The synthesis of a feedback controller of non-linear discrete systems is considered. The control systems designed arc optimal and low sensitive to parameter variations. The first step in the synthesis of the controller is to quasilinearize the non-linear difference equations which describe the nonlinear discrete systems. Dynamic programming is then applied to find the feedback control law with respect to a quadratic performance index which includes the state variable, control variable, trajectory sensitivity function and control sensitivity function as its arguments. The optimal gains in the feedback control law for the non-linear systems are then determined by iteration. An example is studied in detail to show the superiority of this technique over the optimal control system without including the sensitivity functions.