$H_{\infty}$ state feedback control for nonlinear systems with input saturation based on policy iteration

In this paper, we propose an optimal algorithm based on policy iteration (PI), which is used to learn the
$H_{\infty}$
state feedback control solution for nonlinear systems with input saturation. Firstly, The Hamilton-Jacobi-Isaacs (HJI) equation corresponding to the optimal control problem is constructed by a suitable quasi-norm, which can dispose the constraint on the input. Secondly, the PI algorithm is developed to solve the HJI equation without the complete knowledge of internal system dynamics, and an actor-critic-disturbance (ACD) structure neural network (NN) is introduced to implement the PI algorithm. Furthermore, we estimate the ACD-NN weights based on the least-square approach to achieve the optimal solution. Finally, the effectiveness of the PI algorithm is shown on the translational oscillator with rotational actuator (TORA) system and the
$H_{\infty}$
controller guarantees the closed-loop TORA system stability.