Fixed-time parameter estimation in polynomial systems through modulating functions

In this work, a novel procedure for identifying the parameters of a polynomial systems is introduced. In order to get a regression form of the system, and to avoid the necessity of time-derivatives of input/output signals, the modulating function method is applied. In contrast to other available techniques for achieving estimates in finite-time, the real-time inversion of square matrices is not required. Instead, a nonlinear gradient algorithm is used to let the estimate converge in fixed-time. This procedure allows a continuous and recursive update of the parameter estimates and avoids the computational burdens of inversion-based estimation schemes.