# Optimal control of discrete-time switched linear systems via continuous parameterization

## TL;DR

This paper introduces a new optimization-based method for designing optimal controllers for discrete-time switched linear systems, reducing computational complexity by using auxiliary variables and non-smooth optimization techniques.

## Contribution

It proposes a continuous parameterization approach that simplifies the switching law design, enabling more efficient computation compared to traditional methods.

## Key findings

- Reduces computational complexity in switching law design
- Uses auxiliary continuous input variables for optimization
- Demonstrates effectiveness through simulations

## Abstract

The paper presents a novel method for designing an optimal controller for discrete-time switched linear systems. The problem is formulated as one of computing the discrete mode sequence and the continuous input sequence that jointly minimize a quadratic performance index. State-of-art methods for solving such a control problem suffer in general from a high computational requirement due to the fact that an exponential number of switching sequences must be explored. The method of this paper addresses the challenge of the switching law design by introducing auxiliary continuous input variables and then solving a non-smooth block-sparsity inducing optimization problem.