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

نوع مقاله : علمی-پژوهشی

نویسندگان

1 عضو هیات علمی ، گروه مهندسی برق، دانشکده فنی مهندسی، دانشگاه آزاد اسلامی واحد اهواز، ایران

2 گروه کنترل،دانشکده مهندسی برق، دانشگاه صنعتی خواجه نصیرالدین طوسی

3 عضو هیات علمی/ دانشگاه صنعتی شریف

چکیده

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.

کلیدواژه‌ها

عنوان مقاله [English]

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

نویسندگان [English]

  • S. Najafi Birgani 1
  • B. Moaveni 2
  • A. Khaki-Sedigh 3
1 Department of Electrical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 Department of Systems and Control, Faculty of Electrical Engineering, K. N. Toosi University of Technology (KNTU), P.O.Box: 16315-1355, Tehran, Iran
3 Department of Systems and Control, Faculty of Electrical Engineering, K. N. Toosi University of Technology (KNTU), P.O.Box: 16315-1355, Tehran, Iran
چکیده [English]

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.

کلیدواژه‌ها [English]

  • Non-cooperative Differential Game
  • Nash-based Decentralized Control System
  • Infinite Horizon Linear Quadratic Regulator
  • Feedback Nash Equilibrium Point
  • Two-Area Power System

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