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Indirect adaptive control of nonlinearly parameterized nonlinear dissipative systems
Author(s) -
Ortega Romeo,
Cisneros Rafael,
Wang Lei,
Schaft Arjan
Publication year - 2022
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.6078
Subject(s) - control theory (sociology) , mathematics , estimator , parameterized complexity , dissipative system , controller (irrigation) , nonlinear system , adaptive control , dissipation , monotonic function , computer science , mathematical analysis , control (management) , physics , statistics , quantum mechanics , artificial intelligence , agronomy , biology , thermodynamics , combinatorics
In this note we address the problem of indirect adaptive (regulation or tracking) control of nonlinear, input affine dissipative systems. It is assumed that the supply rate, the storage and the internal dissipation functions may be expressed as nonlinearly parameterized regression equations where the mappings (depending on the unknown parameters) satisfy a monotonicity condition—this encompasses a large class of physical systems, including passive systems. We propose to estimate the system parameters using the “power‐balance” equation, which is the differential version of the classical dissipation inequality, with a new estimator that ensures global, exponential, parameter convergence under the very weak assumption of interval excitation of the power‐balance equation regressor. To design the indirect adaptive controller we make the standard assumption of existence of an asymptotically stabilizing controller that depends—possibly nonlinearly—on the unknown plant parameters, and apply a certainty‐equivalent control law. The benefits of the proposed approach, with respect to other existing solutions, are illustrated with examples.