Identification of Switched Linear Systems: Persistence of Excitation and Numerical Algorithms

TL;DR

This paper introduces a weaker persistence of excitation condition for identifying switched linear systems, enabling fewer samples for unique parameter determination and proposing an effective numerical algorithm for the problem.

Contribution

It presents a novel, weaker condition for persistence of excitation that guarantees uniqueness and reduces sample requirements, along with an improved numerical algorithm for system identification.

Findings

Weaker excitation condition guarantees unique parameters with fewer samples.

Surrogate optimization problem has the same solution as the original integer problem.

Proposed algorithm effectively handles unknown number of subsystems.

Abstract

This paper investigates two issues on identification of switched linear systems: persistence of excitation and numerical algorithms. The main contribution is a much weaker condition on the regressor to be persistently exciting that guarantees the uniqueness of the parameter sets and also provides new insights in understanding the relation among different subsystems. It is found that for uniquely determining the parameters of switched linear systems, the minimum number of samples needed derived from our condition is much smaller than that reported in the literature. The secondary contribution of the paper concerns the numerical algorithm. Though the algorithm is not new, we show that our surrogate problem, relaxed from an integer optimization to a continuous minimization, has exactly the same solution as the original integer optimization, which is effectively solved by a block-coordinate descent algorithm. Moreover, an algorithm for handling unknown number of subsystems is proposed. Several numerical examples are illustrated to support theoretical analysis.