Novel adaptive estimation and control of continuous-time systems based on parameter estimation error

This paper studies an alternative adaptive estimation and control approach for continuous-time systems that can be presented in a parameterized form. A novel leakage term containing the parameter estimation error is proposed by introducing filter operations on the system dynamics, and then superimposed in the gradient based adaptive laws to estimate the unknown parameters. Consequently, exponential error convergence can be achieved for both the tracking control and parameter estimations. The proposed control and adaptive law are further modified via the sliding mode approach to achieve finite-time (FT) error convergence. Moreover, appropriate comparisons to gradient method and σ-modification are provided concerning the robustness and estimation performance. Comparative simulations are provided to illustrate the effectiveness of the methods.