# Optimal control of linear systems with limited control actions: threshold-based event-triggered control

## TL;DR

This paper addresses the challenge of limited control message transmission in linear-quadratic optimal control by proposing threshold-based event-triggered mechanisms, exact solutions, heuristics, and stability analysis for receding horizon control.

## Contribution

It introduces an exact solution to a non-convex control problem and develops efficient heuristics, along with stability analysis for event-triggered receding horizon control.

## Key findings

- Exact solution via quadratic programs
- Heuristic algorithms reduce computational complexity
- Stability of receding horizon control established

## Abstract

We consider a finite-horizon linear-quadratic optimal control problem where only a limited number of control messages are allowed for sending from the controller to the actuator. To restrict the number of control actions computed and transmitted by the controller, we employ a threshold-based event-triggering mechanism that decides whether or not a control message needs to be calculated and delivered. Due to the nature of threshold-based event-triggering algorithms, finding the optimal control sequence requires minimizing a quadratic cost function over a non-convex domain. In this paper, we firstly provide an exact solution to the non-convex problem mentioned above by solving an exponential number of quadratic programs. To reduce computational complexity, we, then, propose two efficient heuristic algorithms based on greedy search and the Alternating Direction Method of Multipliers (ADMM) method. Later, we consider a receding horizon control strategy for linear systems controlled by event-triggered controllers, and we also provide a complete stability analysis of receding horizon control that uses finite horizon optimization in the proposed class. Numerical examples testify to the viability of the presented design technique.