Prescribed-Time Adaptive Parameter Estimation for Uncertain Linear Systems via Modified Volterra Operator - Shi, Shang; Min, Huifang; Hu, YinLong (Nonlinear dynamics, 2025)
In this paper, a novel framework is developed to address the parameter estimation problem in uncertain linear systems. Primarily, a new modified Volterra operator is proposed by incorporating a delayed term into the standard Volterra operator. Several properties of the modified Volterra operator are presented, illustrating that the proposed operator offers enhanced robustness against a wide range of uncertainties without requiring an increase in the order of the kernel functions. Building on the modified Volterra operator, we propose a novel adaptive estimation algorithm to achieve precise parameter estimation within a given prescribed time for continuous-time linear systems without uncertainties. Subsequent to this, a robustness analysis for systems subject to output uncertainties is provided. We present a sufficient condition under which the proposed robust estimation algorithm has been shown to achieve enhanced robustness against a wide range of uncertainties. The boundedness of the estimation error is guaranteed for uncertainties that satisfy this condition, including constant, slowly varying, and even some unbounded uncertainties. Additionally, our proposed parameter estimation algorithm only requires the availability of input and output signals, effectively eliminating dependency on unknown initial conditions and high-order derivatives of measurable signals. Finally, simulation comparison is presented to show the effectiveness of the proposed method.