Improved performance of identification and adaptive control schemes using fractional operators

In this article, we address the problem of designing high-performance adaptive schemes for control and identification applications. Specifically, we propose an estimator with two extra degrees of freedom (DOF) and prove that the choice of them enhances the transient and robust performance while keeping the asymptotic convergence. These two DOF appear when one allows a fractional-order for derivatives and integrals in the formal expression of a gradient-like estimator with memory. It is shown that the resulting enhancement in the performance is enlarged when noninteger values are assigned to these DOF. The estimator is used to robustly solve a tracking control problem for uncertain (integer-order) nonlinear dynamical systems in strict-feedback form. A numerical example illustrates that the performance features of the proposed estimator are inherited in the closed-loop behavior.