A parametric sensitivity constrained linear quadratic controller

Abstract

The purpose of this paper is to give a new insight on a suboptimal linear quadratic control taking explicitly into account the parametric uncertainties. System sensitivity to parameter variations is handled through including a quadratic trajectory parametric sensitivity term in the cost functional to be minimized. The paper main contribution is twofold: - Using a descriptor system approach, the paper shows that the underlying singular linear-quadratic optimal control problem leads to a non-standard Riccati equation. - A solution to the proposed control problem is given based on a connection to the so-called Lur'e matrix equations. Some examples are given in order to illustrate the interest of the approach.