Abstraction-based optimal controller synthesis using dynamic quantization and RRT*

This paper addresses the abstraction-based optimal control problems of nonlinear control systems under linear temporal logic (LTL) tasks, and proposes a novel local-to-global controller synthesis approach. First, dynamic quantization techniques and the Rapidly-exploring Random Trees Star (RRT*) algorithm are combined together to generate an optimal sequence of quantization regions, which are further applied to verify the realization of the LTL task and are involved in the optimal control design. Second, with the optimal sequence of quantization regions, the LTL task is decomposed into finite local ones, which are embedded into finite local optimization problems. Third, in order to deal with these local optimization problems, the abstraction-based optimal control approach is developed such that a novel hybrid sub-optimal controller is established to achieve the LTL task. Finally, a numerical example is presented to illustrate the proposed approach.