A mixed PI/VI design method for nonlinear H∞ Control. (1st September 2019)

• Record Type: Journal Article
• Authors: Liu, Lijun; Zhu, Chunhui; Wei, Fang; Yu, Zhen
• Is Part Of: International journal of robust and nonlinear control. Volume 29:Number 17(2019)
• Page Start: 6274
• Page End: 6287
• Publication Date: 2019-09-01
• Subjects: HJI equation -- Lasserre's hierarchy -- nonlinear robust control -- policy iteration -- value iteration; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.4730
• Languages: English
• ISSNs: 1049-8923

Abstract

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.