Optimal control of linear systems with limited control actions: threshold-based event-triggered control
This work addresses the problem of reducing communication in control systems for engineers designing resource-constrained networked control systems.
The paper solves a finite-horizon linear-quadratic optimal control problem with a limited number of control actions using threshold-based event-triggering. It provides an exact solution via exponential quadratic programs and proposes efficient heuristic algorithms (greedy search and ADMM), along with a stability analysis for receding horizon control.
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.