Optimal Decentralized Control with Asymmetric Partial Information Sharing

TL;DR

This paper develops optimal decentralized control strategies for networked control systems with asymmetric partial information sharing, addressing the challenges posed by coupled estimation errors and non-separable information structures.

Contribution

It introduces a novel framework for optimal control under asymmetric information sharing, deriving coupled Riccati equations and proposing iterative and suboptimal solutions.

Findings

Optimal estimators for asymmetric observations are derived.

The control gain depends on the estimation gain, with coupled Riccati equations.

A suboptimal solution is proposed for the complex control problem.

Abstract

This paper considers the optimal decentralized control for networked control systems (NCSs) with asymmetric partial information sharing between two controllers. In this NCSs model, the controller 2 (C2) shares its observations and part of its historical control inputs with the controller 1 (C1), whereas C2 cannot obtain the information of C1 due to network constraints. We present the optimal estimators for C1 and C2 respectively based on asymmetric observations. Since the information for C1 and C2 are asymmetric, the estimation error covariance (EEC) is coupled with the controller which means that the classical separation principle fails. By applying the Pontryagin's maximum principle, we obtain a solution to the forward and backward stochastic difference equations. Based on this solution, we derive the optimal controllers to minimize a quadratic cost function. Combining the optimal controllers with the EEC, the controller C1 is decoupled from the ECC. It should be emphasized that the control gain is dependent on the estimation gain. What's more, the estimation gain satisfies the forward Riccati equation and the control gain satisfies the backward Riccati equation which makes the problem more challenging. We propose iterative solutions to the Riccati equations and give a suboptimal solution to the optimal decentralized control problem.