Optimal Control for a Class of Complex-Valued Nonlinear Systems
In this chapter, an optimal control scheme based on ADP is developed to solve infinite-horizon optimal control problems of continuous-time complex-valued nonlinear systems. A new performance index function is established based on 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. Based on the transformed system and the performance index function, a new ADP method is developed to obtain the optimal control law 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.
- 8.Bolognani, S., Smyshlyaev, A., Krstic, M.: Adaptive output feedback control for complex-valued reaction-advection-diffusion systems, In: Proceedings of American Control Conference, Seattle, Washington, USA, pp. 961–966, (2008)Google Scholar
- 9.Hamagami, T., Shibuya, T., Shimada, S.: Complex-valued reinforcement learning. In: Proceedings of IEEE International Conference on Systems, Man, and Cybernetics, Taipei, Taiwan, pp. 4175–4179 (2006)Google Scholar
- 10.Paulraj, A., Nabar, R., Gore, D.: Introduction to Space-Time Wireless Communications. Cambridge University Press, Cambridge (2003)Google Scholar
- 14.Khalil, H.K.: Nonlinear System. Prentice-Hall, Upper Saddle River (2002)Google Scholar
- 15.Lewis, F.L., Jagannathan, S., Yesildirek, A.: Neural Network Control of Robot Manipulators and Nonlinear Systems. Taylor & Francis, New York (1999)Google Scholar