Time-optimal control for discrete-time hybrid automata

• Published in: International journal of control Vol. 78; no. 11; pp. 847 - 863
• Main Authors: Pang, Y., Spathopoulos, M. P.
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis Group 20.07.2005; Taylor & Francis
• Subjects: Applied sciences; Computer science; control theory; systems; Control system analysis; Control system synthesis; Control theory. Systems; Exact sciences and technology; Optimal control; Convex set; Hybrid control; Control synthesis; Set computation; Linear time; Dynamical system; Reachability analysis; Reachability; Hybrid system; Control constraint; Minimum time; Convex hull; Optimal solution; Discrete time; Discrete programming; Quantifier; Dynamic programming; Time optimal control; Non convex analysis
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207170500114899

In this paper, the problem of time-optimal control for hybrid systems with discrete-time dynamics is considered. The hybrid controller steers all trajectories starting from a maximal set to a given target set in minimum time. We derive an algorithm that computes this maximal winning set. Also, algorithms for the computation of level sets associated with the value function rather than the value function itself are presented. We show that by solving the reachability problem for the discrete time hybrid automata we obtain the time optimal solution as well. The control synthesis is subject to hard constraints on both control inputs and states. For linear discrete-time dynamics, linear programming and quantifier elimination techniques are employed for the backward reachability analysis. Emphasis is given on the computation of operators for non-convex sets using an extended convex hull approach. A two-tank example is considered in order to demonstrate the techniques of the paper.