Temporal logic model predictive control

• Published in: Automatica (Oxford) Vol. 56; pp. 78 - 85
• Main Authors: Aydin Gol, Ebru, Lazar, Mircea, Belta, Calin
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2015
• Subjects: Discrete-time systems; Formal methods; Linear temporal logic; Model predictive control; Discrete-time systems; Model predictive control; Formal methods; Linear temporal logic
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2015.03.029

This paper proposes an optimal control strategy for a discrete-time linear system constrained to satisfy a temporal logic specification over a set of linear predicates in its state variables. The cost is a quadratic function that penalizes the distance from desired state and control trajectories. The specification is a formula of syntactically co-safe Linear Temporal Logic (scLTL), which can be satisfied in finite time. To incorporate dynamic environments, it is assumed that the reference trajectories are only available over a finite horizon and a model predictive control (MPC) approach is employed. The MPC controller solves a set of convex optimization problems guided by the specification and subject to progress constraints. The constraints ensure that progress is made towards the satisfaction of the formula with guaranteed satisfaction by the closed-loop trajectory. The algorithms proposed in this paper were implemented as a software package that is available for download. Illustrative case studies are included.