Robust Optimal Control of Continuous Linear Quadratic System Subject to Disturbances - Wu, Changzhi; Wang, Xiangyu; Teo, Kok Lay; Jiang, L. (Springer, 2014)
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.