Optimal mean decentralized controller design of interconnected systems with randomized information pattern

Abstract

This paper studies the optimal decentralized LQR control problem (ODLCP) of interconnected systems (ISs) with random communication delays. A connected digraph is used to describe the IS. The edges in the graph represent the network connection between the subsystems. Assume that the subsystem information travels across an edge in the graph with random delays. To design the controller gains off-line, the communication outcomes are random and unknown for all subsystems. Thus, the ODLCP is defined under the framework of randomized information pattern. In general, it is difficult to find the global optimal solution to the ODLCP with randomized information pattern, due to the random sparse structure constraints. In this paper, a new information set composed of noise history is found to design the controller without losing optimality. Using the property of the information set we found, the random sparse structure constraints are treated by the Hadamard product. Then, the system state and the control input can be decomposed into independent components. Based on the decomposition results, an optimal controller in the mean sense is designed for the ODLCP with randomized information pattern by solving algebraic Riccati equation and linear matrix equations. The proposed theoretical results are demonstrated by a numerical example.