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Robust performance control of uncertain nonlinear systems: A self‐tuning approach
Author(s) -
Lee T. S.,
Chen B. S.
Publication year - 1994
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.4590040505
Subject(s) - control theory (sociology) , nonlinear system , parametric statistics , mathematics , riccati equation , controller (irrigation) , algebraic riccati equation , robust control , estimator , stability (learning theory) , algebraic number , nonlinear control , differential equation , computer science , control (management) , mathematical analysis , statistics , physics , quantum mechanics , artificial intelligence , machine learning , agronomy , biology
The problem of output regulation with a guaranteed H ∞ performance, besides robust stability, for a class of feedback linearizable nonlinear systems via self‐tuning controllers is investigated. The H ∞ performance consists of the desired disturbance attenuation and internal finite L 2 ‐gain stability. We show that, under the perturbations of matched parametric uncertainties, the sufficient condition for the existence of a self‐tuning controller reduces to the solvability of a single Hamilton‐Jacobi‐Isaacs inequality (or algebraic Riccati equation) which indicates that the design can be performed as if the system uncertainties were absent. Under certain situations, the sufficient condition is also necessary. Once a solution of this nonlinear differential inequality (or algebraic equation) is available, a desired self‐tuning controller with gradient‐type parameter estimator can easily be constructed. The present work falls into the category of singular nonlinear H ∞ control since the desired H ∞ performance does not require any penalty on control input variables. The results also provide an immediate application to H ∞ self‐tuning model reference control in linear systems under full state measurement.