On maximum hands-off restricted hybrid control for discrete-time switched linear systems

TL;DR

This paper introduces a novel algorithm for designing maximum hands-off hybrid control sequences in discrete-time switched linear systems, optimizing sparsity while satisfying system constraints.

Contribution

It presents a new graph-theoretic and linear algebra-based method for synthesizing sparse hybrid control sequences under specific system and control restrictions.

Findings

Successfully designed maximum hands-off control sequences in numerical examples.

The algorithm guarantees control sparsity under certain system conditions.

Demonstrated effectiveness through simulations on example systems.

Abstract

This paper deals with design of maximum hands-off hybrid control sequences for discrete-time switched linear systems. It is a sparsest combination of a discrete control sequence (i.e. the switching sequence) and a continuous control sequence, both satisfying pre-specified restrictions on the admissible actions, that steers a given initial state of the switched system to the origin of the state-space in a pre-specified duration of time. Given the subsystems dynamics, the sets of admissible continuous and discrete control, the initial state and the time horizon, we present a new algorithm that, under certain conditions on the subsystems dynamics and the admissible control, designs maximum hands-off hybrid control sequences for the resulting switched system. The key apparatuses for our analysis are graph theory and linear algebra. Numerical examples are presented to demonstrate our results.