Event-Based ADP Tracking Control of Complex-Valued Nonlinear Systems

This paper addresses the tracking control problem of a complex-valued nonlinear system. First, an augmented complex-valued tracking error system is constructed. By separating the real part and the imaginary part, the augmented complex-valued system is translated into a real-valued augmented system. The tracking control problem of a complex-valued system is converted into an optimal regulation of the real-valued augmented system. An event-based controller is proposed to solve the optimal regulation of the augmented system. Then, an ADP-based framework is used to realize the controller, which is composed of an action network and a critic network. The action network is specially formulated for obtaining control input and the critic network is specially formulated for generating performance value. Both two networks are complex-valued neural networks. Through well-designed event-triggered conditions, the tracking error is proved to be uniformly ultimately bounded (UUB) and the Zeno behaviors are excluded. The algorithm is applied to complex-valued signal tracking to demonstrate its effectiveness.