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A Polynomial Algorithm solving a Special Class of Hybrid Optimal Control Problems

  • Autori: Bauso, D.; Pesenti, R.
  • Anno di pubblicazione: 2006
  • Tipologia: Proceedings (TIPOLOGIA NON ATTIVA)
  • Parole Chiave: AlgorithmsHybrid computersInteger programmingLinear control systems
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Hybrid optimal control problems are, in general, difficult to solve. A current research goal is to isolate those problems that lead to tractable solutions [5]. In this paper, we identify a special class of hybrid optimal control problems which are easy to solve. We do this by using a paradigm borrowed from the Operations Research field. As main result, we present a solution algorithm that converges to the exact solution in polynomial time. Our approach consists in approximating the hybrid optimal control problem via an integer-linear programming reformulation. The integer-linear programming problem is a Set-covering one with a totally unimodular constraint matrix and therefore solving the Setcovering problem is equivalent to solving its linear relaxation. It turns out that any solution of the linear relaxation is a feasible solution for the hybrid optimal control problem. Then, given the feasible solution, obtained solving the linear relaxation, we find the optimal solution via local search