Robust Optimal Control of Wave Energy Converters Based on Adaptive Dynamic Programming

Jing Na, Guang Li, Bin Wang, Guido Herrmann, Siyuan Zhan

Research output: Contribution to journalArticle (Academic Journal)peer-review

10 Citations (Scopus)
357 Downloads (Pure)


This paper presents a robust adaptive optimal control strategy for wave energy converters (WECs). We first propose a new estimator in a simple form to address modeling uncertainties and formulate the control of WECs as an optimal control problem. Then a novel energy maximization control strategy is developed based on the concept of adaptive dynamic programming (ADP), where a critic neural network (NN) is used to approximate the time-dependant optimal cost value. To achieve guaranteed convergence, a recently proposed adaptive law based on the parameter estimation error is further tailored to online update the weights of critic NN. Consequently, the critic NN output, e.g. the costate, can be used to compute the optimal feedback control. The proposed robust ADP WEC control method is not only effective in handling dynamic uncertainties, but also computationally efficient with a very fast online convergence rate for the weights of the critic NN (less than 20 seconds for irregular sea waves as demonstrated in the simulations). These advantages significantly enhance the real-time applicability of the proposed method. Simulation results show that this approach is robust to model uncertainties and has significantly reduced computational costs for implementation.
Original languageEnglish
Number of pages10
JournalIEEE Transactions on Sustainable Energy
Early online date16 Jul 2018
Publication statusE-pub ahead of print - 16 Jul 2018


  • adaptive dynamic programming
  • adaptive optimal control
  • Artificial neural networks
  • Computational modeling
  • Dynamic programming
  • Force
  • Optimal control
  • Robustness
  • Uncertainty
  • uncertainty estimator
  • Wave energy converter

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