Unknown piecewise constant parameters identification with exponential rate of convergence

Abstract

Summary The scope of this research is the identification of unknown piecewise constant parameters of linear regression equation under the finite excitation condition. Compared to the known methods, to make the computational burden lower, only one model to identify all switching states of the regression is used in the developed procedure with the following two‐fold contribution. First of all, we propose a new truly online estimation algorithm based on a well‐known DREM approach to detect switching time and preserve time alertness with adjustable detection delay. Second, despite the fact that a switching signal function is unknown, the adaptive law is derived that provides global exponential convergence of the regression parameters estimates to their true values in case the regressor is finitely exciting somewhere inside the time interval between two consecutive parameters switches. 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

“…Compared to the results of event‐triggered control of switching systems 17‐19 that, at best, translate the observer design problem to the verification of some LMIs and the addition of complicated switching strategies, we provide a full analytic solution to the problem. Moreover, these results rely on the stringent PE condition, which is significantly relaxed here. We improve the results of Reference 20, that also uses DREM‐based observers, replacing the PE assumption by a very weak IE condition and achieving finite convergence time (FCT). Compared to the interesting results of References 22 and 24 where two complex estimators based on DREM, integral filter and resetting filtration techniques 26 were proposed to ensure global exponential estimation of unknown piecewise constant parameters, in this note we present a switched version of the LS‐DREM estimator 25 to guarantee estimation in finite time of unknown switching parameters as well as unmeasurable states. …”

“…However, as recognized by the authors in Reference 23, the resetting operation involves offline operations like the concurrent learning scheme of Reference 8. A significant improvement to this result was later reported in Reference 24 where the resetting is removed and replaced by an ingenuous switching detection scheme. The proof of convergence relies on the condition of IE on each switching sub‐interval.…”

“…In this paper, similar to References 20‐22, and 24, we address the problem of adaptive observer design for LTV systems with switching unknown parameters. In the spirit of the gain‐scheduling and event‐trigger controllers discussed above, we assume the existence of a known gain‐scheduled variable, that identifies the switching instants.…”

“…In the spirit of the gain‐scheduling and event‐trigger controllers discussed above, we assume the existence of a known gain‐scheduled variable, that identifies the switching instants. To carry out the adaptive observer design we combine a new version of the GPEBO technique with an extension of the LS+DREM estimator recently reported in Reference 25 to prove that the system state and the parameters converge in finite time , under the same assumption as Reference 24, that is, IE on each switching subinterval. Two modifications to the standard GPEBO technique are proposed in this paper, first, the inclusion of a feedforward term in the output signal and the addition of a new output‐injection for the observer design, that relaxes the assumption of stability of the homogeneous system (Assumptions 1 and 2 12 ).…”

“…Compared to the interesting results of References 22 and 24 where two complex estimators based on DREM, integral filter and resetting filtration techniques 26 were proposed to ensure global exponential estimation of unknown piecewise constant parameters, in this note we present a switched version of the LS‐DREM estimator 25 to guarantee estimation in finite time of unknown switching parameters as well as unmeasurable states.…”