<p>This paper studies the problem of designing decentralized optimal control strategies for large-scale systems through the integration of a Min–Max Differential Dynamic Programming (DDP) method with mismatched interconnections which are deviations between the modeled and actual interactions among subsystems. The large-scale system dynamics is first decomposed into a set of auxiliary subsystems each with two players. Then, the distributed control for the overall system is obtained by finding the optimal control policies of the auxiliary subsystems, which is achieved through the framework of the Min–Max DDP approach. The convergence of the proposed algorithm is studied, and the control policies are guaranteed to reach their optimal value at the end of the iteration. Furthermore, through the Lyapunov analysis, the convergence of the state of the overall closed-loop system with the decentralized controls is studied. Finally, the proposed algorithm is applied to three practical large-scale systems to showcase its effectiveness.</p>

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Distributed min–max differential dynamic programming for large-scale systems with mismatched interconnections

  • Mohammad Sarbaz,
  • Wei Sun

摘要

This paper studies the problem of designing decentralized optimal control strategies for large-scale systems through the integration of a Min–Max Differential Dynamic Programming (DDP) method with mismatched interconnections which are deviations between the modeled and actual interactions among subsystems. The large-scale system dynamics is first decomposed into a set of auxiliary subsystems each with two players. Then, the distributed control for the overall system is obtained by finding the optimal control policies of the auxiliary subsystems, which is achieved through the framework of the Min–Max DDP approach. The convergence of the proposed algorithm is studied, and the control policies are guaranteed to reach their optimal value at the end of the iteration. Furthermore, through the Lyapunov analysis, the convergence of the state of the overall closed-loop system with the decentralized controls is studied. Finally, the proposed algorithm is applied to three practical large-scale systems to showcase its effectiveness.