Neurodynamic Programming and Tracking Control for Nonlinear Stochastic Systems by PI Algorithm

In this paper, for nonlinear stochastic systems, the optimal tracking control problem (OTCP) is solved by adaptive dynamic programming (ADP) techniques. Firstly, the complex OTCP is transformed into a stable control optimization problem by reconstructing a new stochastic augmented system. Then, simplifying the actor-critic architecture and reducing the computational load, critic neural networks (NNs) is used in iterative learning. And by using Lyapunov method, the ultimate uniform boundedness (UUB) of the tracking system is proved. To be precise, no literature has been published on the OTCP for nonlinear Itô type stochastic systems via the ADP method. This work is the first attempt in this field. Finally, in simulation, the method is applied to sinusoidal waveform and periodic rectangular step signal, and even unbounded exponential waveform.