Design of impulsive adaptive observers for improvement of persistency of excitation

Denis Efimov 1, 2 Alexander Fradkov 3
1 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
2 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : The development of adaptive observer techniques for nonlinear systems in the output canonical form is proposed applying additional impulsive feedback in the observer equations. The stability of new impulsive adaptive observer is investigated. It is shown that under some conditions the proposed impulsive feedback can improve the rate of the observer convergence or relax the requirement on persistency of excitation, which is usually introduced to ensure convergence of the parameter estimates. The proposed feasibility conditions include positivity of dwell time (boundedness of impulse frequency) and solvability of some Lyapunov-like matrix inequalities. The results are illustrated by simulation for three examples (including a single link flexible joint robot example).
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International Journal of Adaptive Control and Signal Processing, Wiley, 2014, pp.1--18. 〈10.1002/acs.2506〉
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Denis Efimov, Alexander Fradkov. Design of impulsive adaptive observers for improvement of persistency of excitation. International Journal of Adaptive Control and Signal Processing, Wiley, 2014, pp.1--18. 〈10.1002/acs.2506〉. 〈hal-01016332〉

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