Modularized Control Synthesis for Complex Signal Temporal Logic Specifications

The control synthesis of a dynamic system subject to signal temporal logic (STL) specifications is commonly formulated as a mixed-integer linear programming (MILP) problem. Solving a MILP problem is computationally expensive when the STL formulas are long and complex. In this paper, we propose a framework to transform a long and complex STL formula into a syntactically separate form, i.e., the logical combination of a series of short and simple subformulas with non-overlapping timing intervals. Using this framework, one can easily modularize the synthesis of a complex formula using the synthesis solutions of the subformulas, which improves the efficiency of solving a MILP problem. Specifically, we propose a group of separation principles to guarantee the syntactic equivalence between the original formula and its syntactically separate counterpart. Then, we propose novel methods to solve the largest satisfaction region and the open-loop controller of the specification in a modularized manner. The efficacy of the methods is validated with a robot monitoring case study in simulation. Our work is promising to promote the efficiency of control synthesis for systems with complicated specifications.