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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.
Song et al. (Tue,) studied this question.