Unknown Piecewise Constant Parameters Identification with Exponential Rate of Convergence

Abstract

The scope of this research is the identification of piecewise constant parameters of linear regression equations under the finite excitation condition. Such an equation is considered as a switched system, which identification usually consists of three main steps: a switching time instant detection, choice of the most appropriate model from the known set or generation of a new one, online adjustment of the chosen model parameters. Compared to the known methods, to make the computational burden lower and simplify the stability analysis, we use only one model to identify all switching states of the regression. So, the proposed identification procedure includes only two main approaches. The first one is a new estimation algorithm to detect switching time and preserve time alertness, which is based on a well-known DREM procedure and ensures adjustable detection delay. Unlike existing solutions, it does not involve an offline operation of data monitoring and stacking. The second one is the adaptive law, which provides element-wise monotonous exponential convergence of the regression parameters to their true values over the time range between two consecutive switches. Its convergence condition is that the regressor is finitely exciting somewhere inside such time interval. The robustness of the proposed identification procedure to the influence of external disturbances is analytically proved.Its effectiveness is demonstrated via numerical experiments, in which both abstract regressions and a second-order plant model are used.

Adaptive state observation of linear time‐varying systems with switching unknown parameters: Application to gain scheduling and event‐triggered control

“…We now proceed to design a simple gain-scheduled stabilizing controller and place the system in closed-loop. Toward this end, we observe that we can rewrite the system (24) in the form…”