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A family of H ∞ controllers for dissipative Hamiltonian systems
Author(s) -
Xu Song,
Hou Xiaorong
Publication year - 2011
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1753
Subject(s) - dissipative system , hamiltonian (control theory) , cascade , control theory (sociology) , hamiltonian system , mathematics , computer science , control (management) , mathematical analysis , mathematical optimization , physics , engineering , quantum mechanics , chemical engineering , artificial intelligence
SUMMARY Using structure properties of dissipative Hamiltonian systems, this paper investigates the parameterization problem of H infty controllers for such systems. A family of H ∞ controllers with full information is first obtained by interconnecting an H ∞ controller with a generalized zero‐energy‐gradient (ZEG) detectable, free generalized Hamiltonian system. Then, a family of H ∞ controllers with partial information is presented in terms of the solution to an inequality only in 2 n independent variables (twice as many as the one used to characterize the state feedback) and without imposing an additional cascade condition. Both of the parameterization methods avoid solving Hamilton–Jacobi–Issacs equations (or inequalities), and thus the proposed controllers are relatively simple in form and easy in operation. Numerical experiments show the effectiveness and feasibility of the proposed methods. Copyright © 2011 John Wiley & Sons, Ltd.