Adaptive dynamic programming for H∞ control of constrained-input nonlinear systems

This paper presents a novel adaptive/approximate dynamic programming algorithm to solve the H∞ control problem of constrained-input continuous-time nonlinear systems. The developed algorithm employs a single critic neural network (NN) to derive the approximate solution of the Hamilton-Jacobi-Isaacs equation. With two additional terms introduced, namely, the stabilizing term and the robustifying term to update the critic NN, no initial stabilizing control is required. Meanwhile, the developed critic tuning rule not only ensures that the optimal saddle point can be obtained but also guarantees stability of the closed-loop system. In addition, all signals in the closed-loop system are proved to be uniformly ultimately bounded via Lyapunov´s direct method. Finally, an illustrate example is provided to verify the effectiveness of the developed approach.