Data-Based Approximate Optimal Control for Unknown Nonaffine Systems via Dynamic Feedback

In this paper, an integral reinforcement learning (IRL)-based approximate optimal control (AOC) method for unknown nonaffine systems is developed by using dynamic feedback. For optimal control problems of nonaffine systems, optimal control policy cannot be expressed explicitly since the input gain matrix is unknown. Therefore, the nonaffine system is transformed into an augmented affine system by introducing a dynamic feedback signal as the virtual control input. Moreover, by designing an appropriate value function for the augmented affine system, the optimal control of augmented affine system is formulated as the AOC for unknown nonaffine systems. Moreover, the IRL method is adopted to derive the approximate solution of Hamilton-Jacobi-Bellman equation via the critic-only structure. Theoretical analysis concludes that the closed-loop system is uniformly ultimately bounded by using the developed IRL-based AOC scheme. An example is utilized to demonstrate the effectiveness of the present approach.