Data-driven Nonlinear MIMO ADP Method and Its Application in PMSM Control

Authors

  • Bowen Sui  Lab of Intelligent Control and Computation, Shanghai Maritime University, Shanghai, 201306, China

DOI:

https://doi.org//10.32628/IJSRSET196644

Keywords:

Adaptive Dynamic Programming(ADP), Data-driven, Intelligent power systems, Permanent Magnet Synchronous Motor (PMSM), Nonlinear systems, Multiple Input Multiple Output systems(MIMO).

Abstract

The power system is a nonlinear, time-varying, high-dimensional system. How to carry out effective control to ensure its safer and more stable operation has been the subject of many scholars' research, and with the continuous expansion of the power system scale and randomness. With the access of stronger new energy sources, the challenges facing the security and stability of power systems are becoming more and more severe. The conventional optimal control method has certain limitations. For example, the variational method can only solve the optimal problem that the control quantity is not constrained. The maximal/minimum value principle can only solve the optimal control problem described by ordinary differential equations. Although the plan can solve the more general optimal control problem than that described by the ordinary differential equation, it is a problem of dimensionality hazard because it is a time-backward algorithm. Adaptive dynamic programming is the product of the integration of artificial intelligence and control technology. Its essence is to approximate the solution of Hamilton-Jacobi-Bellman equation by using the approximate structure of the function of the neural network. This method does not depend on the mathematical model of the controlled object, nor does it need to define the performance index accurately, and can learn online. The introduction of this method into the power system can provide a new idea for the non-linear optimal control of the power system. Based on the traditional Adaptive Dynamic Programming (ADP) algorithm, this paper proposes a data-driven nonlinear Multi-Input and Multi-Output (MIMO) adaptive dynamic programming algorithm, and applies this algorithm to Permanent Magnet Synchronous Motor (PMSM) related control. The simulation of single objective control and under-actuated control model proves that the data-driven adaptive dynamic programming method based on least squares strategy iteration has strong robustness.

References

  1. DUNIN-BARKOWSKI W L, WUNSCH D C. Phase-based storage of information in the cerebellum J. Neurocomputing, 1999, s 26–27(26-27): 677-685.
  2. LIU D, HG Z. A neural dynamic programming approach for learning control of failure avoidance problems M. 2005.
  3. WERBOS P J. Using ADP to Understand and Replicate Brain Intelligence: the Next Level Design; proceedings of the IEEE International Symposium on Approximate Dynamic Programming and Reinforcement Learning, F, 2007 C.
  4. WATKINS C J C H. Learning from Delayed Rewards J. Robotics & Autonomous Systems, 1989, 15(4): 233-235.
  5. PROKHOROV D V, WUNSCH D C. Adaptive critic designs J. IEEE Transactions on Neural Networks, 1997, 8(5): 997.
  6. LANDELIUS T. Reinforcement Learning and Distributed Local Model Synthesis J. Linkoping University Sweden, 1997,
  7. SCHERRER B. Asynchronous neurocomputing for optimal control and reinforcement learning with large state spaces J. Neurocomputing, 2005, 63(1-4): 229-251.
  8. WERBOS P J. Advanced Forecasting Methods for Global Crisis Warning and Models of Intelligence J. General Systems Yearbook, 1977, 22(6): 25-38.
  9. WERBOS P J. Approximate dynamic programming for real-time control and neural modeling J. Handbook of Intelligent Control Neural Fuzzy & Adaptive Approaches, 1992,
  10. BERTSEKAS D P, TSITSIKLIS J N. Neuro-Dynamic Programming M. Athena Scientific, 1996.
  11. TANG H. Performance Potential-based Neuro-dynamic Programming for SMDPs J. Acta Automatica Sinica, 2005, 31(4): 642-645.
  12. ZHANG H, LUO Y, LIU D. A New Fuzzy Identification Method Based on Adaptive Critic Designs J. Lecture Notes in Computer Science, 2006, 3971(804-809.
  13. NASCIMENTO J, POWELL W B. An Optimal Approximate Dynamic Programming Algorithm for Concave, Scalar Storage Problems With Vector-Valued Controls J. IEEE Transactions on Automatic Control, 2013, 58(12): 2995-3010.
  14. WERBOS P. Beyond Regression : New Tools for Prediction and Analysis in the Behavioral Science J. Phddissertation Harvard University, 1974, 29(18): 65-78.
  15. BERTSEKAS D P, TSITSIKLIS J N, VOLGENANT A. Neuro-Dynamic Programming J. Encyclopedia of Optimization, 1996, 27(6): 1687-1692.
  16. PROKHOROV D V, WUNSCH D C. Adaptive critic designs J. IEEE Transactions on Neural Networks, 1997, 8(5): 997-1007.
  17. SI J, WANG Y T. On-Line Learning Control by Association and Reinforcement; proceedings of the Ieee-Inns-Enns International Joint Conference on Neural Networks, F, 2000 C.
  18. ENNS R, SI J. Apache Helicopter Stabilization Using Neural Dynamic Programming J. Journal of Guidance Control & Dynamics, 2002, 25(1): 19-25.
  19. ENNS R, SI J. Helicopter trimming and tracking control using direct neural dynamic programming J. IEEE Transactions on Neural Networks, 2003, 14(4): 929-939.
  20. MURRAY J J, COX C J, LENDARIS G G, et al. Adaptive dynamic programming J. Systems Man & Cybernetics Part C Applications & Reviews IEEE Transactions on, 2002, 32(2): 140-153.
  21. LEE J M, LEE J H. Approximate dynamic programming-based approaches for input–output data-driven control of nonlinear processes M. Pergamon Press, Inc., 2005.
  22. PADHI R, UNNIKRISHNAN N, WANG X, et al. A single network adaptive critic (SNAC) architecture for optimal control synthesis for a class of nonlinear systems J. Neural Networks the Official Journal of the International Neural Network Society, 2006, 19(10): 1648.
  23. ALTAMIMI A, LEWIS F L, ABUKHALAF M. Discrete-time nonlinear HJB solution using approximate dynamic programming: convergence proof J. IEEE Transactions on Systems Man & Cybernetics Part B Cybernetics A Publication of the IEEE Systems Man & Cybernetics Society, 2008, 38(4): 943-949.
  24. DIERKS T, THUMATI B T, JAGANNATHAN S. Optimal control of unknown affine nonlinear discrete-time systems using offline-trained neural networks with proof of convergence M. Elsevier Science Ltd., 2009.
  25. ERKS T, JAGANNATHAN S. Online Optimal Control of Affine Nonlinear Discrete-Time Systems With Unknown Internal Dynamics by Using Time-Based Policy Update J. IEEE Trans Neural Netw Learn Syst, 2012, 23(7): 1118-1129.
  26. HEYDARI A, BALAKRISHNAN S N. Global optimality of approximate dynamic programming and its use in non-convex function minimization M. Elsevier Science Publishers B. V., 2014.
  27. SILVER D, HUANG A, MADDISON C J, et al. Mastering the game of Go with deep neural networks and tree search J. Nature, 2016, 529(7587): 484.
  28. GRANTER S R, BECK A H, JR P D. AlphaGo, Deep Learning, and the Future of the Human Microscopist J. Archives of Pathology & Laboratory Medicine, 2017, 141(5): 619.
  29. WANG F Y, ZHANG H, LIU D. Adaptive Dynamic Programming: An Introduction J. IEEE Computational Intelligence Magazine, 2009, 4(2): 39-47.

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Published

2019-12-30

Issue

Section

Research Articles

How to Cite

[1]
Bowen Sui, " Data-driven Nonlinear MIMO ADP Method and Its Application in PMSM Control, International Journal of Scientific Research in Science, Engineering and Technology(IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 6, Issue 6, pp.175-186, November-December-2019. Available at doi : https://doi.org/10.32628/IJSRSET196644