H ∞ optimal control of unknown linear systems by adaptive dynamic programming with applications to time‐delay systems
Huaiyuan Jiang, Bin Zhou, Shuai Liu · International Journal of Robust and Nonlinear Control · 2021
Abstract In this paper, a new value iteration (VI) based method is proposed to solve the H ∞ control problem of continuous‐time linear systems. The problem is transformed into solving a nonlinear differential equation, and the local stability of its solution is proved. Then a VI based iteration scheme for getting the approximation of the H ∞ optimal controller is proposed. Compared with the existing results, the proposed scheme does not need any special initial matrix or extra condition to solve the problem and provides a relatively small disturbance attenuation bound. The related result is also applied to the quadratic guaranteed cost control of linear time‐delay systems. Simulation examples verify the effectiveness of the proposed schemes.