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Optimal Control for a Class of Complex-Valued Nonlinear Systems

  • Ruizhuo SongEmail author
  • Qinglai Wei
  • Qing Li
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 166)

Abstract

In this chapter, an optimal control scheme based on ADP is developed to solve infinite-horizon optimal control problems of continuous-time complex-valued nonlinear systems. A new performance index function is established based on complex-valued state and control. Using system transformations, the complex-valued system is transformed into a real-valued one, which overcomes Cauchy–Riemann conditions effectively. Based on the transformed system and the performance index function, a new ADP method is developed to obtain the optimal control law using neural networks. A compensation controller is developed to compensate the approximation errors of neural networks. Stability properties of the nonlinear system are analyzed and convergence properties of the weights for neural networks are presented. Finally, simulation results demonstrate the performance of the developed optimal control scheme for complex-valued nonlinear systems.

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Copyright information

© Science Press, Beijing and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.University of Science and Technology BeijingBeijingChina
  2. 2.Institute of AutomationChinese Academy of SciencesBeijingChina

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