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Stability of the equilibria of adaptive systems with leakage estimator
Author(s) -
Ortega Romeo,
Espinosa Gerardo
Publication year - 1991
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.4480050303
Subject(s) - control theory (sociology) , estimator , mathematics , lti system theory , exponential stability , controller (irrigation) , stability (learning theory) , state estimator , adaptive estimator , limiting , adaptive control , work (physics) , linear system , computer science , engineering , mathematical analysis , physics , control (management) , nonlinear system , thermodynamics , statistics , mechanical engineering , agronomy , quantum mechanics , artificial intelligence , machine learning , biology
We study the stability of the equilibria of the differential equations that describe an adaptive controller in closed loop with a linear time‐invariant (LTI) undermodelled plant when the parameter update law is a leaky gradient, i.e. a s̀‐modified estimator. Hsu and Costa studied the full‐order case and showed that under certain limiting conditions the resulting dynamic system has three, possibly unstable, equilibrium points. Here we provide a modest extension to that work by further characterizing the class of undermodelled LTI plants for which the equilibria exist and are (un)stable Interestingly enough, it is shown that the equilibria are stable iff a given compensator stabilizes the plant. This compensator is, up to the plant ‘steady state gain’, known to the designer.