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Adaptive state feedback control by orthogonal approximation functions
Author(s) -
Del Vecchio D.,
Marino R.,
Tomei P.
Publication year - 2002
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.709
Subject(s) - mathematics , a priori and a posteriori , control theory (sociology) , approximation error , adaptive control , norm (philosophy) , state vector , state (computer science) , tracking error , upper and lower bounds , mathematical optimization , computer science , algorithm , control (management) , mathematical analysis , epistemology , classical mechanics , philosophy , physics , artificial intelligence , political science , law
For a class of feedback linearizable systems a state feedback adaptive control based on orthogonal approximation functions is designed, under the assumption of matching conditions for the uncertainties and of known bounds on a given compact set for the unknown non‐linear function. By virtue of Bessel inequality, the bound on the unknown non‐linear function gives a bound on the norm of the optimal weight vector for any choice of the number of approximating functions, which allows us to design a robust state feedback adaptive scheme with parameter projections. The resulting control algorithm has several advantages over available schemes: it does not require a priori bounds on the approximation error and on the optimal weight vector; it is repeatable, since the set of initial conditions for the state and the parameter estimates from which a class of reference signals is tracked is explicitly given; it characterizes the L ∞ and L 2 performance of the tracking error in terms of both the approximation and the parameter estimation error; it gives full flexibility in the choice of the number of approximating orthogonal functions. Copyright © 2002 John Wiley & Sons, Ltd.