This paper presents the first robust adaptive backstepping control system for dynamical systems whose functional uncertainties are assumed to lie in a user-defined native space (also known as reproducing kernel Hilbert space). This work generalizes classical adaptive backstepping control systems and their non-adaptive counterparts by freeing the user from providing a parametric representation of the functional uncertainties. Such representations are usually in the form of regressor vectors, or some equivalent structure, to be provided a priori or reconstructed online, and without employing conservative upper bounds on the functional uncertainties. The adaptive laws for the proposed control system are shown to form a distributed parameter system (DPS) evolving over the native space. Finite-dimensional approximations of such adaptive laws enable their applications to problems of practical interest, as shown by the proposed numerical examples.

Robust Adaptive Backstepping Control Over Native Spaces / Orlando, G. A.; L'Afflitto, A.; Kurdila, A. J.. - In: IEEE CONTROL SYSTEMS LETTERS. - ISSN 2475-1456. - 9:(2025), pp. 859-864. [10.1109/LCSYS.2025.3578938]

Robust Adaptive Backstepping Control Over Native Spaces

Orlando G. A.;
2025

Abstract

This paper presents the first robust adaptive backstepping control system for dynamical systems whose functional uncertainties are assumed to lie in a user-defined native space (also known as reproducing kernel Hilbert space). This work generalizes classical adaptive backstepping control systems and their non-adaptive counterparts by freeing the user from providing a parametric representation of the functional uncertainties. Such representations are usually in the form of regressor vectors, or some equivalent structure, to be provided a priori or reconstructed online, and without employing conservative upper bounds on the functional uncertainties. The adaptive laws for the proposed control system are shown to form a distributed parameter system (DPS) evolving over the native space. Finite-dimensional approximations of such adaptive laws enable their applications to problems of practical interest, as shown by the proposed numerical examples.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/3001323