A Linear Quadratic Controller Design Incorporating a Parametric Sensitivity Constraint

Abstract

The purpose of this paper is to propose a synthesis method of parametric sensitivity constrained linear quadratic (SCLQ) controller for an uncertain linear time invariant (LTI) system. System sensitivity to parameter variation is handled through an additional quadratic trajectory parametric sensitivity term in the standard LQ criterion to be minimized. The main purpose here is to find a suboptimal linear quadratic control taking explicitly into account the parametric uncertainties. The paper main contribution is threefold: 1) A descriptor system approach is used to show that the underlying singular linear-quadratic optimal control problem leads to a non-standard Riccati equation. 2) A solution to the proposed control problem is then given based on a connection to the so-called Lur’e matrix equations. 3) A synthesis method of multiple parametric SCLQ controllers is proposed to cover the whole parametric uncertainty while degrading as less as possible the intrinsic robustness properties of each local linear quadratic controller. Some examples are presented in order to illustrate the effectiveness of the approach.