Risk-constrained linear quadratic control with one-step delayed sharing information pattern

This paper studies the linear quadratic control for non-Gaussian interconnected systems (ISs). A nonclassical information pattern called delayed sharing pattern is considered. Most existing literature on linear quadratic control with delayed sharing pattern considers only the average event performance. However, the low-probability, yet extreme event may significantly damage the system. With explicit incorporation of a risk constraint, we design a best linear controller to balance the tradeoff between average and extreme event performance, which is referred to as the risk-constrained best linear controller (RcBLC). We extend the projection principle of random variables. Through the extended projection principle and the Lagrangian duality theory, we establish a framework, in which the RcBLC can be designed by solving two tractable optimization subproblems with the optimal Lagrange multiplier found by the binary search method. Based on the established framework, we develop efficient design algorithms for the proposed RcBLC. Finally, the merit of the proposed method is illustrated by numerical simulation on a two-UAV system.