Decentralized Control of Linear Systems with Private Input and Measurement Information

TL;DR

This paper develops a novel decentralized control approach for linear systems with private input and measurement data, achieving asymptotic optimality without requiring access to other regulators' historical inputs.

Contribution

Introduces new observers and decentralized controllers for linear systems with private information, providing asymptotic optimality and advancing classical decentralized control methods.

Findings

Decentralized controllers are asymptotically optimal.

New observers effectively utilize private input and measurement data.

Results are fundamental to classical decentralized control.

Abstract

In this paper, we study the linear quadratic (LQ) optimal control problem of linear systems with private input and measurement information. The main challenging lies in the unavailability of other regulators' historical input information. To overcome this difficulty, we introduce a kind of novel observers by using the private input and measurement information and accordingly design a kind of new decentralized controllers. In particular, it is verified that the corresponding cost function under the proposed decentralized controllers are asymptotically optimal as comparison with the optimal cost under optimal state-feedback controller. The presented results in this paper are new to the best of our knowledge, which represent the fundamental contribution to classical decentralized control.