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We consider a finite-horizon linear-quadratic optimal control problem whereonly a limited number of control messages are allowed for sending from thecontroller to the actuator. To restrict the number of control actions computedand transmitted by the controller, we employ a threshold-based event-triggeringmechanism that decides whether or not a control message needs to be calculatedand delivered. Due to the nature of threshold-based event-triggeringalgorithms, finding the optimal control sequence requires minimizing aquadratic cost function over a non-convex domain. In this paper, we firstlyprovide an exact solution to the non-convex problem mentioned above by solvingan exponential number of quadratic programs. To reduce computationalcomplexity, we, then, propose two efficient heuristic algorithms based ongreedy search and the Alternating Direction Method of Multipliers (ADMM)method. Later, we consider a receding horizon control strategy for linearsystems controlled by event-triggered controllers, and we also provide acomplete stability analysis of receding horizon control that uses finitehorizon optimization in the proposed class. Numerical examples testify to theviability of the presented design technique.

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