Robust Optimal Control of Continuous Linear Quadratic System Subject to Disturbances

Abstract

In this chapter, the robust optimal control of linear quadratic system is considered. This problem is first formulated as a minimax optimal control problem. We prove that it admits a solution. Based on this result, we show that this infinite-dimensional minimax optimal control problem can be approximated by a sequence of finite-dimensional minimax optimal parameter selection problems. Furthermore, these finite-dimensional minimax optimal parameter selection problems can be transformed into semi-definite programming problems or standard minimization problems. A numerical example is presented to illustrate the developed method.