Abstract
The problem addressed in this paper is the control of a class of SISO feedback linearizable systems containing unknown nonlinearities with known bound on a given compact set. The unknown nonlinearities are locally approximated by a finite sum of Orthogonal basis functions so that by virtue of Bessel inequality a bound on the norm of the optimal weights derives directly from the bound of the nonlinearity. Projection algorithms can then be used to assure that the parameters estimates remain inside the set in which the optimal weights lie. The proposed control algorithm is repeatable since the set of initial conditions for which given performances are guaranteed is explicitly determined; no a priori knowledge on the bound of the norm of the optimal weights is required.
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© 2001 Springer-Verlag London Limited
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Del Vecchio, D., Marino, R., Tomei, P. (2001). Adaptive control of feedback linearizable systems by orthogonal approximation functions. In: Isidori, A., Lamnabhi-Lagarrigue, F., Respondek, W. (eds) Nonlinear control in the Year 2000. Lecture Notes in Control and Information Sciences, vol 258. Springer, London. https://doi.org/10.1007/BFb0110225
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DOI: https://doi.org/10.1007/BFb0110225
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