Robust Explicit Time Optimal Controllers for Linear Systems Via Decomposition Principle

One of the key problems in time optimal control (TOC) is the inherent computational complexity, which restricts its application to low dimensional systems. Considering a constrained linear system with bounded disturbances, this paper proposes a novel approach to reduce the computational complexity of TOC, where the terminal controller is nonlinear. It comprises several predetermined local linear feedback laws, resulting in a large terminal set. Starting from this relatively large terminal set, a large domain of attraction of the proposed TOC controller can be obtained by using a short horizon, and consequently leads to a low on-line computational effort. Furthermore, by formulating a suitable cost function, as time evolves, the TOC controller reaches the desired controller to obtain a good asymptotical behavior. The performance of the proposed approach is assessed via a numerical example.