Learning event-driven switched linear systems

TL;DR

This paper introduces an automata-based learning algorithm for identifying black-box switched linear systems with event-driven switching logic, extending Angluin's L* algorithm to infer the system's automaton.

Contribution

It presents a novel automata-theoretic approach for learning switched linear systems with event-driven logic, combining system simulation with automata inference techniques.

Findings

Successfully learned system automata from benchmark examples

Demonstrated effectiveness of the algorithm in identifying switching logic

Extended Angluin's L* algorithm for system identification

Abstract

We propose an automata theoretic learning algorithm for the identification of black-box switched linear systems whose switching logics are event-driven. A switched system is expressed by a deterministic finite automaton (FA) whose node labels are the subsystem matrices. With information about the dimensions of the matrices and the set of events, and with access to two oracles, that can simulate the system on a given input, and provide counter-examples when given an incorrect hypothesis automaton, we provide an algorithm that outputs the unknown FA. Our algorithm first uses the oracle to obtain the node labels of the system run on a given input sequence of events, and then extends Angluin's \(L^*\)-algorithm to determine the FA that accepts the language of the given FA. We demonstrate the performance of our learning algorithm on a set of benchmark examples.