Adaptive observer design for time-varying nonlinear systems with unknown polynomial parameters

Many control methods involve the use of real-time values of the vector of state variables or its estimates. The article considers the problem of state variables observer design for a nonlinear non-stationary plant of a wider class compared to the known analogs. To solve the problem, some assumptions are introduced and assume that the plant parameters are partially unknown functions of time that have a polynomial form. Each unknown parameter is polynomial functions of time with unknown coefficients. The problem of observer design is solved in a class of identification methods that involve the transformation of the original nonlinear mathematical model of the plant to a linear static regression. In this problem, instead of the usual unknown constant parameters, there are unknown functions of time which are estimated. To recover variables of unknown parameters, the method of dynamic regressor extension and mixing (DREM) is used. The method allows getting monotone estimates, as well as accelerating the convergence of estimates to true values. The proposed approach allows obtaining accurate parametrizations of a nonlinear nonstationary system, including exponentially decaying terms associated with using dynamic filters. The resulting regression equations explicitly depend on the tuning parameters and changing the values of these parameters yields a system of linearly independent regression equations, which can be decomposed then into scalar regression equations. An observer of the parameters and state variables of the system is designed on the basis of scalar regression equations and considered assumptions about models of non-stationary parameters. The application of the proposed approach allows solving the problems of restoring unmeasured variables and signals of real control systems and also makes it possible to identify unknown time-varying parameters, which in turn is an actual self-contained problem. The approach can be applied in control of chemical processes, electrical converters, as well as in a number of other technical applications

Adaptive observer for state variables of a time-varying nonlinear system with unknown constant parameters and delayed measurements

Unknown constant parameters estimation problem for a nonlinear time-varying system with delayed measurements is considered. The objective of this work is to design an adaptive observer for a nonlinear time-varying system. The observer must provide asymptotic convergence of the unknown constant parameters estimates to their true values. The main idea behind the method is to perform the parametrization of initial dynamical system based on GPEBO (Generalized Parameter Estimation Based Observer) technology and to build a linear regression model. The identification of linear regression model unknown parameters is performed using least square method with forgetting factor. This work develops the previously published approach for the case of nonlinear time-varying systems with delayed measurements. New parameters estimation algorithm can be applied for technical tasks, such as technical condition control and automatic control systems design

An Adaptive Observer-Based Controller Design for Active Damping of a DC Network with a Constant Power Load

© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksThis article explores a nonlinear, adaptive controller aimed at increasing the stability margin of a direct-current (dc), small-scale, electrical network containing an unknown constant power load (CPL). Due to its negative incremental impedance, this load reduces the effective damping of the network, which may lead to voltage oscillations and even to voltage collapse. To overcome this drawback, we consider the incorporation of a controlled dc-dc power converter in parallel with the CPL. The design of the control law for the converter is particularly challenging due to the existence of unmeasured states and unknown parameters. We propose a standard input-output linearization stage, to which a suitably tailored adaptive observer is added. The good performance of the controller is validated through experiments on a small-scale network.Peer ReviewedPostprint (author's final draft

CONTROL APPROACH FOR NONLINEAR PLANT WITH PARAMETRIC UNCERTAINTIES AND INPUT DELAY

Stabilization problem for unstable nonlinear plant with parametric uncertainties and input delay is considered. A new approach is proposed that makes it possible to identify plant parameters and design the stabilization algorithm with state-feedback predictor

ADAPTIVE OUTPUT CONTROL: SUBJECT MATTER, APPLICATION TASKS AND SOLUTIONS

The problem of adaptive output control for parametric and functionally uncertain plants is considered. Application examples illustrating the practical use of the discussed theory are given along with the mathematical formulation of the problem. A brief review of adaptive output control methods, by both linear and non-linear systems, is presented and an extensive bibliography, in which the reader will find a detailed description of the specific algorithms and their properties, is represented. A new approach to the output control problem - a method of consecutive compensator - is considered in detail

Finite-time parameter estimation without persistence of excitation

International audienceThe problem of adaptive estimation of constant parameters in the linear regressor model is studied without the hypothesis that regressor is Persistently Excited (PE). First, the initial vector estimation problem is transformed to a series of the scalar ones using the method of Dynamic Regressor Extension and Mixing (DREM). Second, several adaptive estimation algorithms are proposed for the scalar scenario. In such a case, if the regressor may be nullified asymptotically or in a finite time, then the problem of estimation is also posed on a finite interval of time. The efficiency of the proposed algorithms is demonstrated in numeric experiments for an academic example

Frequency estimation of a sinusoidal signal with time-varying amplitude

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On robust parameter estimation in finite-time without persistence of excitation

International audienceThe problem of adaptive estimation of constant parameters in the linear regressor model is studied without the hypothesis that regressor is Persistently Excited (PE). First, the initial vector estimation problem is transformed to a series of the scalar ones using the method of Dynamic Regressor Extension and Mixing (DREM). Second, several adaptive estimation algorithms are proposed for the scalar scenario. In such a case, if the regressor may be nullified asymptotically or in a finite time, then the problem of estimation is also posed on a finite interval of time. Robustness of the proposed algorithms with respect to measurement noise and exogenous disturbances is analyzed. The efficiency of the designed estimators is demonstrated in numeric experiments for academic examples