Decentralized Stochastic Linear-Quadratic Optimal Control with Risk Constraint and Partial Observation

TL;DR

This paper develops a decentralized stochastic LQ control framework with risk constraints and partial observations, providing explicit solutions and stability conditions, and demonstrating effectiveness through numerical examples.

Contribution

It introduces a novel risk-constrained decentralized LQ control model with partial observations and unreliable communication, deriving explicit solutions and stability criteria.

Findings

Explicit solutions for finite and infinite horizon problems.

Necessary and sufficient conditions for mean-square stability.

Effective numerical examples demonstrating the approach.

Abstract

This paper addresses a risk-constrained decentralized stochastic linear-quadratic optimal control problem with one remote controller and one local controller, where the risk constraint is posed on the cumulative state weighted variance in order to reduce the oscillation of system trajectory. In this model, local controller can only partially observe the system state, and sends the estimate of state to remote controller through an unreliable channel, whereas the channel from remote controller to local controllers is perfect. For the considered constrained optimization problem, we first punish the risk constraint into cost function through Lagrange multiplier method, and the resulting augmented cost function will include a quadratic mean-field term of state. In the sequel, for any but fixed multiplier, explicit solutions to finite-horizon and infinite-horizon mean-field decentralized linear-quadratic problems are derived together with necessary and sufficient condition on the mean-square stability of optimal system. Then, approach to find the optimal Lagrange multiplier is presented based on bisection method. Finally, two numerical examples are given to show the efficiency of the obtained results.