A Fully Automated Framework for Control of Linear Systems from LTL Specifications

• Published in: Hybrid Systems: Computation and Control pp. 333 - 347
• Main Authors: Kloetzer, Marius, Belta, Calin
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2006; Springer
• Series: Lecture Notes in Computer Science
• Subjects: Applied sciences; Atomic Proposition; Automata. Abstract machines. Turing machines; Computer science; control theory; systems; Control theory. Systems; Exact sciences and technology; Feedback Controller; Linear Temporal Logic; Software; Software engineering; Temporal Logic; Theoretical computing; Transition System; Bounded control; Closed loop; State feedback; Control synthesis; Continuous time; State space method; Linear control; Temporal logic; Program verification; Hybrid system; Polyhedron; Linear logic; Closed systems; Transition system; Discrete time; Model checking; Trajectory
• ISBN: 3540331700; 9783540331704
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11730637_26

We consider the following problem: given a linear system and an LTL − − X formula over a set of linear predicates in its state variables, find a feedback control law with polyhedral bounds and a set of initial states so that all trajectories of the closed loop system satisfy the formula. Our solution to this problem consists of three main steps. First, we partition the state space in accordance with the predicates in the formula and construct a transition system over the partition quotient, which captures our capability of designing controllers. Second, using model checking, we determine runs of the transition system satisfying the formula. Third, we generate the control strategy. Illustrative examples are included.