Robust Decentralized Control System Design based on Nash Equilibrium Point using Linear Quadratic Regulators

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Najafi Birgani S.; Moaveni B.; Khaki Sedigh A.

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Paper Information

Journal: TABRIZ JOURNAL OF ELECTRICAL ENGINEERING Year:2022 | Volume: | Issue: Page(s): 51-60

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Information Journal Paper

Title

Robust Decentralized Control System Design based on Nash Equilibrium Point using Linear Quadratic Regulators

Author(s)

Najafi Birgani S. | Moaveni B. | Khaki Sedigh A. | Issue Writer Certificate

Keywords

Non-cooperative Differential GameQ4

Nash-based Decentralized Control SystemQ4

Infinite Horizon Linear Quadratic RegulatorQ4

Feedback Nash Equilibrium PointQ4

Two-Area Power SystemQ4

Abstract

Non-cooperative intelligent control agents (ICAs) with dedicated cost functions, can lead the system to poor performance and in some cases, closed-loop instability. A robust solution to this challenge is to place the ICAs at the Feedback Nash Equilibrium Point (FNEP) of the differential game between them. This paper introduces the designation of a robust decentralized infinite horizon LQR control system based on the FNEP for a linear time-invariant system. For this purpose, two control strategies are defined. The first one is a centralized infinite horizon LQR (CIHLQR) problem (i.e. a supervisory problem), and the second one is a decentralized control problem (i.e. an infinite horizon linear-quadratic differential game). Then, while examining the optimal solution of each of the above strategies on the performance of the other, the necessary and sufficient conditions for the equivalence of the two problems are presented. In the absence of the conditions, by using the least-squares error criterion, an approximated CIHLQR controller is presented. It is shown that the theorems could be extended from a two-agent control system to a multi-agent system. Finally, the results are evaluated using the simulation results of a Two-Area non-reheat power system.

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