Procedure of identification of piecewise-constant unknown parameters with improved convergence

The research is aimed at improvement of the solution quality of the unknown piecewise-constant parameters identification problem for the classical linear regression equation. To solve this problem, a new procedure to process such equation, which is based on the known method of integral dynamic extension and mixing (I-DREM) but with the interval-based integral filter with exponential forgetting and resetting, is proposed. As proved in the paper, when the I-DREM procedure is applied, the proposed filter, unlike known from the literature, allows one to generate the regression equation with a scalar regressor and adjustable level of disturbance, which is caused by the step-like change of the unknown parameters. The main result of the study is a procedure to process a linear regression equation with a vector regressor, which allows one to derive an adaptation law. If the condition of the regressor finite excitation is met, then such a law guarantees that the identification error of the piecewise-constant parameters is bounded by an adjustable value. All of the aforementioned properties are proved analytically and/or demonstrated via the numerical experiments.