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Learning switched systems from simulation models

The design of decision and control strategies for switched systems typically requires complete knowledge of (i) mathematical models of the subsystems and (ii) restrictions on admissible switches between the subsystems. We propose an active learning algorithm that infers (i) and (ii) for discrete-time switched systems whose subsystems dynamics are governed by sets of scalar polynomials and switching signals are constrained by automata. We collect data from gray-box simulation models of the switched systems for this purpose. Our technique for learning (i) involves linear algebraic tools, while for learning (ii) we employ a modified version of the well-known $L^*$-algorithm from machine learning literature. A numerical example is presented to demonstrate our learning algorithm.

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