Adaptive Dynamic Programming for a Class of Complex-Valued Nonlinear Systems

In this brief, an optimal control scheme based on adaptive dynamic programming (ADP) is developed to solve infinite-horizon optimal control problems of continuous-time complex-valued nonlinear systems. A new performance index function is established on the basis of complex-valued state and control....

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems 2014-09, Vol.25 (9), p.1733-1739
Main Authors: Song, Ruizhuo, Xiao, Wendong, Zhang, Huaguang, Sun, Changyin
Format: Article
Language:English
Subjects:
Adaptive critic designs
adaptive dynamic programming (ADP)
approximate complex-valued systems
Approximation error
Compensation
Computer simulation
Dynamic programming
Dynamical systems
Economic models
Learning systems
Neural networks
Nonlinear dynamics
Nonlinear systems
Optimal control
Optimization
Performance analysis
Performance indices
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Summary:In this brief, an optimal control scheme based on adaptive dynamic programming (ADP) is developed to solve infinite-horizon optimal control problems of continuous-time complex-valued nonlinear systems. A new performance index function is established on the basis of 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. With the transformed system and the performance index function, a new ADP method is developed to obtain the optimal control law by 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.
ISSN:2162-237X
2162-2388
DOI:10.1109/TNNLS.2014.2306201