Robust adaptive parameter estimator design for a multi-sinusoidal signal with fixed-time stability and guaranteed prescribed performance boundary of estimation error

Abstract

In online parameter estimation, fast and accurate estimation without dependence on the initial conditions with good transient properties is an essential issue. Hence, in this paper, a robust adaptive parameter estimation method is proposed that not only can estimate online the unknown parameters of a multi sinusoidal signal in a finite-time without dependence on the initial conditions but also can guarantee the transient and steady-state performance of the estimated parameters with a predefined boundary. At first, to estimate the frequency, offset, phase and amplitude, the multi-sinusoidal signal is represented in a linear regression form. Then, by defining an auxiliary regressor matrix and vector derived by the original regressor vector and output signal, the estimation error is computed indirectly. By employing this parameter estimation error and utilizing the fixed-time stability property of the terminal sliding mode method and Prescribed-Performance concept, robust adaptation laws are designed in such a way that the convergence time of the estimation error is finite so that its settling time is independent from the initial guess, and this time can be predefined. Moreover the estimation error boundary can be predefined. Furthermore, in this method, only the output measurement is needed and there is no need for any observer or predictor. Using the Lyapunov stability theorem it is proved that the estimation error converges to zero when the measurement is free of noise and for the noisy case the estimation error is uniformly ultimately bounded and converges to a compact set around the origin. Three illustrative examples are provided to demonstrate the advantages and effectiveness of the designed estimation laws compared to some existing methods. Simulation results show that the proposed method can estimate the unknown parameters in fixed-time with a pre-adjustable estimation error boundary, even in the presence of measurement noise and confirms the superiority of the proposed method compared to the two existing methods.