Time-constrained temporal logic control of multi-affine systems. (English) Zbl 1302.93113

Aydin Gol, Ebru; Belta, Calin

Nonlinear Anal., Hybrid Syst. 10, 21-33 (2013).

In the paper, the following problem is considered: Given a multi–affine control system and syntactically co–safe Linear Temporal Logic (LTL) formula over rectangular subregions of the state space, find a set of initial states for which there exists a control strategy such that all the trajectories of the closed–loop system satisfy the formula within a given bound. Syntactically co–safe LTL formulas can be used to describe finite horizon specification such as target reachability with obstacles avoidance: ”always avoid obstacle O until reaching target T”, sequencing constraints ”go to C and not go to A or B unless C was visited before”, and more complex temporal and Boolean combinations of these.
The authors describe in detail the control strategy based on deterministic Büchi automata. An iterative refinement procedure via a random optimization algorithm is proposed. Also two examples are given. Computational experiments can be performed using the authors’ Matlab program conPAS available for download from the webside hyness.bu.edu/software.

Reviewer: Wiesław Kotarski (Sosnowiec)

MSC:

93B52	Feedback control
93B05	Controllability
49K15	Optimality conditions for problems involving ordinary differential equations
68Q70	Algebraic theory of languages and automata
90C25	Convex programming

Keywords:

multi–afine systems; control design; linear temporal logic; automata theory

Software:

conPAS; Matlab

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