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On the numerical solution of the control problem of switched linear systems

This paper presents a method to compute an epsilon-optimal solution of the control problem of switched linear systems. A difficulty that emerges in the evaluation of the optimal solution is that the cardinality of the solution set increases exponentially as long as the time-horizon increases linearly, which turns the problem intractable when the horizon is sufficiently large. We propose a numerical method to overcome such difficulty, in the sense that our approach allows the evaluation of epsilon-optimal solutions with corresponding sets that do not increase exponentially.