A mixed PI/VI design method for nonlinear H∞ Control. (1st September 2019) - Liu, Lijun; Zhu, Chunhui; Wei, Fang; Yu, Zhen
Summary: This paper proposes a new mixed policy iteration and value iteration (PI/VI) design method for nonlinear H ∞ control based on the theories of polynomial optimization and Lasserre's hierarchy. The design of a mixed PI/VI controller can be carried out in four steps: firstly, initialize design parameters and expand nonlinear system matrices; secondly, obtain a polynomial matrix inequality for policy improvement; thirdly, obtain the Lasserre's hierarchy of a global polynomial optimization problem for value improvement; fourthly, perform the mixed PI/VI algorithm to approximate the optimal nonlinear H ∞ control law. The novelty of this work lies in that the problem of designing a nonlinear H ∞ controller is translated into a polynomial global optimization problem, which can be solved by Lasserre's hierarchy directly, and then, the mixed PI/VI algorithm is presented to approximate the optimal nonlinear H ∞ control law by updating global optimizers iteratively. The main results of this paper consist of the mixed PI/VI algorithm and the related three theorems, which guarantee robust stability and performance of the closed‐loop nonlinear system. Numerical simulations show that the mixed PI/VI algorithm converges very fast and achieves good robust stability and performance in transient behavior, disturbance rejection, and enlarging the domain of attraction of the close‐loop system.