Order reduction in optimal event-triggered control design for linear stochastic systems

This paper considers the optimal design of event-triggered controllers under a non-traditional average-cost criterion with costly observations. Determining the optimal event-triggering law can be cast in the dynamic programming framework. Due to the lack of a closed form solution for the value function associated with the dynamic program, the methods for calculating the optimal solution suffer from the curse of dimensionality. Based on structural properties of the optimal solution, we develop a novel approximative method to reduce the dimensionality of the underlying optimization problem from the state dimension of the regulated process to the number of control inputs. As processes often consist of only few inputs compared to the number of state variables, such approach reduces the computational complexity significantly. It is shown that the proposed approximative event-trigger preserves the asymptotic behavior of the closed-loop system. A conditions is derived, when the reduced event-triggering law equals the optimal solution. We propose a measure to evaluate the approximation accuracy of the developed order reduction method.