Dynamic Quantization based Control Synthesis for Signal Temporal Logics Specifications

Abstract

For dynamical systems under temporal logic tasks, the control objective is mainly to propose control methods for temporal logic tasks. Existing methods are based on the assumption where temporal logic tasks are realizable, which is not always valid and results in the separation between the realizability verification and the controller design. In this paper, we apply dynamic quantization techniques to propose a framework to combine the verification of signal temporal logic (STL) specifications and the controller design. In particular, a sequence of quantization regions is generated to show the realizability of the STL formula, and results in the decomposition of the global STL formula into finite local ones. All local STL formulas are formulated into optimization problems, which are solved iteratively and result in local controllers, whose combination gives the global controller for the satisfaction of the STL formula. Finally, a numerical example is presented to illustrate the proposed approach.