Hierarchical Controller Synthesis Under Linear Temporal Logic Specifications Using Dynamic Quantization

Linear temporal logic (LTL) is an intuitive and expressive language to specify complex control tasks, and how to design an efficient control strategy for LTL specification is still a challenge. In this paper, we implement the dynamic quantization technique to propose a novel hierarchical control strategy for nonlinear control systems under LTL specifications. Based on the regions of interest involved in the LTL formula, an accepting path is derived first to provide a high-level solution for the controller synthesis problem. Second, we develop a dynamic quantization based approach to verify the realization of the accepting path. The realization verification results in the necessity of the controller design and a sequence of quantization regions for the controller design. Third, the techniques of dynamic quantization and abstraction-based control are combined together to establish the local-to-global control strategy. Both abstraction construction and controller design are local and dynamic, thereby resulting in the potential reduction of the computational complexity. Since each quantization region can be considered locally and individually, the proposed hierarchical mechanism is more efficient and can solve much larger problems than many existing methods. Finally, the proposed control strategy is illustrated via two examples from the path planning and tracking problems of mobile robots.