Discrete-Valued Control by Sum-of-Absolute-Values Optimization

TL;DR

This paper introduces a novel discrete-valued control design method for linear systems using sum-of-absolute-values optimization, providing theoretical guarantees and a fast algorithm for real-time implementation.

Contribution

The paper formulates a finite-horizon SOAV optimal control problem, establishes conditions for its solutions, and develops an ADMM-based algorithm for efficient computation.

Findings

The method guarantees existence, discreteness, and uniqueness of control solutions.

The value function's continuity ensures stability of the control system.

Simulation confirms the effectiveness and real-time applicability of the approach.

Abstract

In this paper, we propose a new design method of discrete-valued control for continuous-time linear time-invariant systems based on sum-of-absolute-values (SOAV) optimization. We first formulate the discrete-valued control design as a finite-horizon SOAV optimal control, which is an extended version of L1 optimal control. We then give simple conditions that guarantee the existence, discreteness, and uniqueness of the SOAV optimal control. Also, we give the continuity property of the value function, by which we prove the stability of infinite-horizon model predictive SOAV control systems. We provide a fast algorithm for the SOAV optimization based on the alternating direction method of multipliers (ADMM), which has an important advantage in real-time control computation. A simulation result shows the effectiveness of the proposed method.