Finite-time Parameter Estimation in Adaptive Control of Nonlinear Systems

In most adaptive control algorithms, parameter estimate errors are not guaranteed to converge to zero. This lack of convergence adversely affects the global performance of the algorithms. The effect is more pronounced in control problems where the desired reference set-point or trajectory depends on the system´s unknown parameters. In this paper, we present a parameter estimation routine that allows exact reconstruction of the unknown parameters in finite time provided a given excitation condition is satisfied. The algorithm is independent of the control and identifier structure employed. The true parameter value is obtained without requiring the measurement or computation of the velocity state vector. The technique provides a direct solution to the problem of removing auxiliary perturbation signals when parameter convergence is achieved. The effectiveness of the proposed method is illustrated with simulation examples.