Value Iteration-Based H∞ Controller Design for Continuous-Time Nonlinear Systems Subject to Input Constraints

In this paper, a novel integral reinforcement learning method is proposed based on value iteration (VI) to design the <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> controller for continuous-time nonlinear systems subject to input constraints. To confront the control constraints, a nonquadratic function is introduced to reconstruct the <inline-formula> <tex-math notation="LaTeX">${L_{2}}$ </tex-math></inline-formula>-gain condition for the <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control problem. Then, the VI method is proposed to solve the corresponding Hamilton–Jacobi–Isaacs equation initialized with an arbitrary positive semi-definite value function. Compared with most existing works developed based on policy iteration, the initial admissible control policy is no longer required which results in a more free initial condition. The iterative process of the proposed VI method is analyzed and the convergence to the saddle point solution is proved in a general way. For the implementation of the proposed method, only one neural network is introduced to approximate the iterative value function, which results in a simpler architecture with less computational load compared with utilizing three neural networks. To verify the effectiveness of the VI-based method, two nonlinear cases are presented, respectively.