LTL receding horizon control for finite deterministic systems

• Published in: Automatica (Oxford) Vol. 50; no. 2; pp. 399 - 408
• Main Authors: Ding, Xuchu, Lazar, Mircea, Belta, Calin
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-02-2014; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Computer simulation; Control system synthesis; Control systems; Control theory. Systems; Exact sciences and technology; Finite deterministic systems; Formal methods; Horizon; Logical, boolean and switching functions; Mathematical analysis; Mathematical models; Model predictive control; Optimal control; Specifications; Tasks; Temporal logic; Theoretical computing; Model predictive control; Finite deterministic systems; Formal methods; Optimal control; Formal method; Control synthesis; Linear time; Real time; Temporal logic; Finite horizon; Linear logic; Time varying system; Deterministic system; Open ended horizon; Reward; Optimal control (mathematics)
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2013.11.030

This paper considers receding horizon control of finite deterministic systems, which must satisfy a high level, rich specification expressed as a linear temporal logic formula. Under the assumption that time-varying rewards are associated with states of the system and these rewards can be observed in real-time, the control objective is to maximize the collected reward while satisfying the high level task specification. In order to properly react to the changing rewards, a controller synthesis framework inspired by model predictive control is proposed, where the rewards are locally optimized at each time-step over a finite horizon, and the optimal control computed for the current time-step is applied. By enforcing appropriate constraints, the infinite trajectory produced by the controller is guaranteed to satisfy the desired temporal logic formula. Simulation results demonstrate the effectiveness of the approach.