H_∞ optimal control of unknown linear systems by adaptive dynamic programming with applications to time-delay systems

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.