A structure-preserving algorithm for the minimum H∞ norm computation of finite-time state feedback control problem

Authors: Wu, Zhi-Gang¹; Zhong, Wan-Xie¹

Source: International Journal of Control, Volume 82, Number 4, April 2009 , pp. 773-781(9)

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Abstract:

The algorithm being developed here is based on the generating function approach for finite-time H∞ control and application of canonical transformation of linear Hamiltonian system. First, an equivalent finite-time H∞ control law in terms of the third-type generating function is derived. Then, by using symplectic structure of the Hamiltonian system's state transition matrix, a group of matrix recursive formulae are deduced for the evaluation of the finite-time H∞ control law. Combining with a matrix singularity testing procedure, this recursive algorithm verifies the existence condition of sub-optimal H∞ controllers and gives the minimum H∞ norm of finite-time control systems. Inherited from the canonical transformation, the matrix recursive formulae have a standard symplectic form; this structure-preserving property helps facilitate reliable and effective computation. Numerical results show the effectiveness of the proposed algorithm.

Keywords: H∞ control; H∞ norm; generating function; canonical transformation; Hamiltonian system; differential Riccati equations

Document Type: Research article

DOI: 10.1080/00207170802294639

Affiliations: 1: State Key Lab of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, China