A polynomial adaptive estimator for nonlinearly parameterized systems

We propose a new polynomial adaptive estimator (PAE) algorithm to estimate parameters that occur nonlinearly. The estimator is based on a polynomial nonlinearity in the Lyapunov function, which is chosen so as to guarantee stability and parameter convergence in systems with polynomial nonlinearity in the unknown parameters. We further extend the PAE algorithm to discretized-parameter polynomial adaptive estimator (DPAE) to achieve stability in general Lipschitz continuous nonlinear functions. We establish the nonlinear persistent excitation (NLPE) condition for parameter convergence using both the PAE and the DPAE.