A New Probabilistic Robust Control Approach for System with Uncertain Parameters

This paper addresses the issues of conservativeness and computational complexity of robust control. A new probabilistic robust control method is proposed to design a high performance controller. The key of the new method is that the uncertainty set is divided into two parts: r ‐subset and the complementary set of r ‐subset. The contributions of the new method are as follows: (i) a deterministic robust controller is designed for r ‐subset, so it has less conservative than those designed by using deterministic robust control method for the full set; and (ii) the probabilistic robustness of the designed controller is evaluated just for the complementary set of r ‐subset but not for the full set, so the computational complexity of the new method is reduced. Given expected probability robustness, a pertinent probabilistic robust controller can be designed by adjusting the norm boundary of r ‐subset. The effectiveness of the proposed method is verified by the simulation example.