Kybernetika 59 no. 1, 28-44, 2023

Performance analysis of least squares algorithm for multivariable stochastic systems

Ziming Wang, Yiming Xing and Xinghua ZhuDOI: 10.14736/kyb-2023-1-0028

Abstract:

In this paper, we consider the parameter estimation problem for the multivariable system. A recursive least squares algorithm is studied by minimizing the accumulative prediction error. By employing the stochastic Lyapunov function and the martingale estimate methods, we provide the weakest possible data conditions for convergence analysis. The upper bound of accumulative regret is also provided. Various simulation examples are given, and the results demonstrate that the convergence rate of the algorithm depends on the parameter dimension and output dimension.

Keywords:

least squares, martingale theory, non-persistent excitation

Classification:

93A10, 93E12, 93E24

paper.pdf

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