Convergence analysis of a synchronous gradient estimation scheme for time-varying parameter systems

Abstract

For the problem of time-varying parameter estimation and its convergence, this paper proposes an invariant matrix to represent the changing laws of time-varying parameters, which suggests a novel expression to describe the parameters by employing finite terms. A joint recursive least squares algorithm is derived by minimizing the criterion function associated with the unknown invariant matrix. For a class of time-varying systems, a joint stochastic gradient algorithm with the computational efficiency is obtained by analogy to achieve the estimation of invariant matrix and system parameters. The convergence analysis is explored to demonstrate that the time-varying parameter estimation error is bounded under the persistent excitation conditions. The simulation results also validate the effectiveness of the proposed synchronous parameter estimation approach.