Optimal control of interconnected systems with time-correlated noises: application to vehicle platoon

Abstract

This paper studies the optimal state-feedback LQG control (OSLC) of interconnected systems (ISs) with time-correlated process noises. In an IS, the information is transmitted among subsystems via the network, and the transmission time is proportional to the distance of the corresponding subsystem pairs. This means that the information received by a subsystem includes the non-real-time information, and that the information from different subsystems may be of different time indexes. This makes the optimal controller design challenging. The OSLC of ISs with time-uncorrelated process noises is studied by an independence decomposition method in the existing literature. However, the existing independence decomposition method strongly relies on the condition that the process noises are time-uncorrelated, and fails for the time-correlated process noises case. In this paper, the globally optimal LQG controller of ISs with time-correlated process noises is successfully designed. In particular, a new cost function decomposition is obtained based on the Bellman equation. Both the system state and the control input are decomposed into two independent parts by the orthogonal decomposition technique. The proposed decomposition method leads to the successful design of the globally optimal controller. The proposed theoretical results are applied to a vehicle platoon system. The simulation shows that the platoon maintains a desired state and achieves a good performance under the proposed controller.