Optimal Controls for Dual-Driven Load System with Synchronously Approximate Dynamic Programming Method

  • Yongfeng Lv
  • Xuemei RenEmail author
  • Linwei Li
  • Jing Na
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 528)


This paper applies a synchronously approximate dynamic programming (ADP) scheme to solve the Nash controls of the dual-driven load system (DDLS) with different motor properties based on game theory. First, a neural network (NN) is applied to approximate the dual-driven servo unknown system model. Because the properties of two motors are different, they have different performance indexes. Another NN is used to approximate performance index function of each motor. In order to minimize the performance index, the Hamilton function is constructed to solve the approximate optimal controls of the load system. Based on parameter error information, an adaptive law is designed to estimate NN weights. Finally, the practical DDLS is simulated to demonstrate that the optimal control inputs can be studied by ADP algorithm.


Servo system Approximate dynamic programming Nash equilibrium Multi-input system Neural networks 



The work was supported by National Natural Science Foundation of China (No. 61433003 and No. 61273150).


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.School of AutomationBeijing Institute of TechnologyBeijingChina
  2. 2.Faculty of Mechanical & Electrical EngineeringKunming University of Science & TechnologyKunmingChina

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