Parameter identification of the normal flow equation by using adaptive estimation

We address the problem of estimating the constant parameters involved in the normal flow equation, which is a Hamilton-Jacobi PDE widely used in many different research areas. The identification of such parameters allows one to estimate the flow function, which is the velocity vector field that governs the dynamics of the level sets associated with the solution of the equation. The estimates are obtained by using a Luenberger observer and a parameter estimator based on the adaptation law proposed by Pomet and Praly in 1992. Such a law makes it possible to explicitly take into account bounds on the parameters. Conditions for the stability of the parameter estimation error are established. Simulation results are presented that confirm the theoretical achievements.