Language-Guided Controller Synthesis for Linear Systems

This paper considers the problem of controlling discrete-time linear systems from specifications given as formulas of syntactically co-safe linear temporal logic over linear predicates in the state variables. A systematic procedure is developed for the automatic computation of sets of initial states and feedback controllers such that all the resulting trajectories of the closed-loop system satisfy the given specifications. The procedure is based on the iterative construction and refinement of an automaton that enforces the satisfaction of the formula. Linear programming based approaches are proposed to compute the polytope-to-polytope controllers that label the transitions of the automaton. Extensions to discrete-time piecewise affine systems and specifications given as formulas of full linear temporal logic are included. The algorithms developed in this paper were implemented as a software package that is available for download. Their application and effectiveness are demonstrated for several case studies.