Time optimal control systhesis for discrete time hybrid automata

Y. Pang, M.P. Spathopoulos

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)847-863
Number of pages16
JournalInternational Journal of Control
Issue number11
Publication statusPublished - 20 Jul 2005


  • control engineering
  • dynamical systems
  • control systems


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