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Generalized nonlinear ℋ︁ ∞ synthesis condition with its numerically efficient solution
Author(s) -
Zheng Qian,
Wu Fen
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.1682
Subject(s) - nonlinear system , bottleneck , polynomial , nonlinear control , mathematics , mathematical optimization , sequential quadratic programming , lyapunov function , control theory (sociology) , computer science , quadratic programming , control (management) , mathematical analysis , physics , quantum mechanics , artificial intelligence , embedded system
In this paper, we will first derive a general synthesis condition for the output‐feedback ℋ ∞ control of smooth nonlinear systems. Computationally efficient ℋ ∞ control design procedure for a subclass of smooth nonlinear systems with polynomial vector field is then proposed by converting the resulting Hamilton‐Jacobi‐Isaacs inequalities from rational forms to their equivalent polynomial forms. Using quadratic Lyapunov functions, both the state‐feedback and output‐feedback problems will be reformulated as semi‐definite optimization conditions and locally tractable solutions can be obtained through sum‐of‐squares (SOS) programming. The proposed nonlinear ℋ ∞ design approach achieves significant relaxations on the plant structure compared with existing results in the literature. Moreover, the SOS‐based solution algorithm provides an effective computational scheme to break the bottleneck in solving nonlinear ℋ ∞ and optimal control problems. The proposed nonlinear ℋ ∞ control approach has been applied to several examples to demonstrate its advantages over existing nonlinear control techniques and its usefulness to engineering problems. Copyright © 2010 John Wiley & Sons, Ltd.