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Strict Lyapunov Functions for Model Reference Adaptive Control: Application to Lagrangian Systems

Abstract : Model reference adaptive control is a well-understood and popular method used in the case when the plant's constant parameters are unknown and must be identified. The related literature is very rich and there exist many proofs of stability and convergence. Lyapunov functions for such systems, having the property that the total derivative is negative definite, are, however, very scarce. In this note we use the Mazenc construction to design a simple strict Lyapunov function in a rather intuitive manner, based on a first-choice function whose derivative is negative semidefinite. Furthermore, we provide, for the first time in the literature, a Lyapunov function for a popular passivity-based adaptive controller for Lagrangian systems.
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Antonio Loria, Elena Panteley, Mohamed Maghenem. Strict Lyapunov Functions for Model Reference Adaptive Control: Application to Lagrangian Systems. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2019, 64 (7), pp.3040-3045. ⟨10.1109/TAC.2018.2874723⟩. ⟨hal-02367693⟩

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