Learning switched systems from simulation models

TL;DR

This paper introduces an active learning method to infer models and switching rules of discrete-time switched systems using simulation data, combining linear algebra and automata learning techniques.

Contribution

It presents a novel active learning algorithm that infers both subsystem models and switching constraints from simulation data, applicable to scalar polynomial systems.

Findings

Successfully infers subsystem dynamics from simulation data

Learns switching constraints using a modified $L^*$-algorithm

Demonstrates effectiveness with a numerical example

Abstract

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.