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Alexey Bobtsov

Publications and source records attributed to Alexey Bobtsov.

At least 19 recordsLinked to original sources
arXiv2026

Observer Design for a Class of Systems Described by Differential-Algebraic Equations and Parameter Identification of an Unmeasured Disturbance

This paper addresses the problem of observer design for a class of linear descriptor systems affected by a certain class of unknown unmatched disturbances. The objective is to estimate the components of the state vector, as well as the unknown parameters of the unmeasured disturbance. To solve this problem, structural assumptions are introduced under which an observer for the dynamic part of the state vector is constructed. Then, based on the obtained state estimate, the disturbance signal is reconstructed, and its unknown parameters are identified. A new parameterization method is proposed for a class of disturbance input signals that depend nonlinearly on unknown parameters, making it possible to obtain a linear regression in the corresponding unknowns. Numerical simulations are presented to demonstrate the effectiveness of the proposed procedures.

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arXiv2026

An Algebraic State Observer for a Self-Sensing Active Magnetic Bearing System

The problem of designing a globally stable observer for a self-sensing active magnetic bearing system assuming only measurements of currents and voltages is addressed in this paper. Towards this end, we first design a radically different, high performance, state observer, which is obtained invoking novel techniques. Indeed, our objective is to obtain an algebraic relation between the unmeasurable part of the state and filtered versions of the systems inputs and outputs, which holds for all times. Then, using this algebraic observer, we propose a robust asymptotic version of the observer. Simulation results that illustrate the performance of the observer are also presented.

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arXiv2026

An Algebraic State Observer for a Class of Physical Systems

In this paper we present a radically new approach to design state observers for nonlinear systems, with particular emphasis on physical ones. Our objective is to obtain an algebraic relation between the unmeasurable part of the state and filtered versions of the systems inputs and outputs, which holds true for all $t \geq 0$. The latter qualifier should be contrasted with the usual asymptotic (or fixed/finite time) objective. The standing assumption for our design is the availability -- or possibility of constructing, via coordinate change -- state components with measurable derivatives. In the physical systems studied in the paper this condition is naturally satisfied. The next step in the design is the application of the Swapping Lemma to pull out from the dynamics the derivative of one of these signals. The design is completed replacing the latter by the measurable signals and arranging the remaining terms. The algebraic observer constitutes a refreshing major departure from classical asymptotic observer designs, even in the case of electrical motors and mechanical systems that have been exhaustively studied. Particularly notable is the fact that no observability or excitation condition is imposed for the construction of the algebraic observer.

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arXiv2025

Adaptive Compensation of Nonlinear Friction in Mechanical Systems Without Velocity Measurement

Friction is an unavoidable phenomenon that exists in all mechanical systems incorporating parts with relative motion. It is well-known that friction is a serious impediment for precise servo control, hence the interest to devise a procedure to compensate for it -- a subject that has been studied by many researchers for many years. The vast majority of friction compensation schemes reported in the literature rely on the availability of velocity measurements, an information that is hard to obtain. A second limitation of the existing procedures is that they rely on mathematical models of friction that contain several unknown parameters, some of them entering nonlinearly in the dynamic equations. In this paper we propose a globally convergent tracking controller for a mechanical system perturbed by static and Coulomb friction, which is a reliable mathematical model of the friction phenomenon, that does not rely one measurement of velocity. The key component is an immersion and invariance-based adaptive speed observer, used for the friction compensation. To the best of our knowledge, this is the first globally convergent solution to this challenging problem. We also present simulation results of the application of our observer for systems affected by friction, which is described by the more advanced LuGre model.

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arXiv2025

Interturn Fault Detection in IPMSMs: Two Adaptive Observer-based Solutions

In this paper we address the problem of online detection of inter-turn short-circuit faults (ITSCFs) that occur in permanent magnet synchronous motors (PMSMs). We propose two solutions to this problem: (i) a very simple linear observer and (ii) a generalized parameter estimation based observer, that incorporates a high performance estimator -- with both observers detecting the short-circuit current and the fault intensity. Although the first solution guarantees the detection of the fault exponentially fast, the rate of convergence is fully determined by the motor parameters that, in some cases, may be too slow. The second observer, on the other hand, ensures finite convergence time under the weakest assumption of interval excitation. To make the observers adaptive, we develop a parameter estimator that, in the case of isotropic PMSMs, estimates on-line (exponentially fast) the resistance and inductance of the motor. It should be underscored that, in contrast with existing observers (including the widely popular Kalman filter) that provide indirect information of the fault current, our observers provide explicit one -- namely the amplitude of the fault current. The performance of both observers, in their linear and generalized parameter estimation-based versions, is illustrated with realistic simulation studies.

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arXiv2024

Immersion of General Nonlinear Systems Into State-Affine Ones for the Design of Generalized Parameter Estimation-Based Observers: A Simple Algebraic Procedure

Generalized parameter estimation-based observers have proven very successful to deal with systems described in state-affine form. In this paper, we enlarge the domain of applicability of this method proposing an algebraic procedure to immerse} an $n$-dimensional general nonlinear system into and $n_z$-dimensional system in state affine form, with $n_z>n$. First, we recall the necessary and sufficient condition for the solution of the general problem, which requires the solution of a partial differential equation that, moreover, has to satisfy a restrictive injectivity condition. Given the complexity of this task we propose an alternative simple algebraic method to identify the required dynamic extension and coordinate transformation, a procedure that, as shown in the paper, is rather natural for physical systems. We illustrate the method with some academic benchmark examples from observer theory literature -- that, in spite of their apparent simplicity, are difficult to solve with the existing methods -- as well as several practically relevant physical examples.

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arXiv2024

State Observer for the Fourth-order Model of a Salient Pole Synchronous Generator with Stator Losses: Known and Partially Unknown Input Cases

In this paper we study the question of how to reconstruct the state of a power system using Phasor Measurement Units (PMUs). In our previous research we proved that this question has an affirmative answer imposing some rather strict structural assumptions: namely, neglecting the generator rotors saliency and assuming that the stator resistance of the synchronous generator is zero. It was shown in simulations that the performance of the proposed observer was sensitive to these assumptions, observing a transient quality degradation for realistic simulations not imposing these assumptions. Moreover, it was assumed in our previous work that the mechanical power and the field voltage are available for measurement, a scenario that it is not always realistic. In this paper we accomplish two ambitious objectives. First, we propose a new observer that does not impose the simplifying assumptions on the generator model. Secondly, we consider the more realistic scenario where only mechanical power is available for measurement. That is, we solve a problem of state reconstruction of a nonlinear system with partially known input measurements -- that is well-known to be a very challenging task. The design of the first observer relies on two recent developments proposed by the authors, a parameter estimation based approach to the problem of state estimation and the use of the Dynamic Regressor Extension and Mixing (DREM) technique to estimate these parameters. The use of DREM allows us to overcome the problem of lack of persistent excitation that stymies the application of standard parameter estimation designs. On the other hand, the observer for the partial input measurement scenario relies on the clever exploitation of the systems model. Simulation results illustrates the good performance of the proposed observers.

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arXiv2024

Parameter identification algorithm for a LTV system with partially unknown state matrix

In this paper an adaptive state observer and parameter identification algorithm for a linear time-varying system are developed under condition that the state matrix of the system contains unknown time-varying parameters of a known form. The state vector is observed using only output and input measurements without identification of the unknown parameters. When the state vector estimate is obtained, the identification algorithm is applied to find unknown parameters of the system.

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arXiv2023

On-line Parameter Estimation of the Polarization Curve of a Fuel Cell with Guaranteed Convergence Properties: Theoretical and Experimental Results

In this paper, we address the problem of online parameter estimation of a Proton Exchange Membrane Fuel Cell (PEMFC) polarization curve, that is the static relation between the voltage and the current of the PEMFC. The task of designing this estimator -- even off-line -- is complicated by the fact that the uncertain parameters enter the curve in a highly nonlinear fashion, namely in the form of nonseparable nonlinearities. We consider several scenarios for the model of the polarization curve, starting from the standard full model and including several popular simplifications to this complicated mathematical function. In all cases, we derive separable regression equations -- either linearly or nonlinearly parameterized -- which are instrumental for the implementation of the parameter estimators. We concentrate our attention on on-line estimation schemes for which, under suitable excitation conditions, global parameter convergence is ensured. Due to these global convergence properties, the estimators are robust to unavoidable additive noise and structural uncertainty. Moreover, their on-line nature endows the schemes with the ability to track (slow) parameter variations, that occur during the operation of the PEMFC. These two features -- unavailable in time-consuming off-line data-fitting procedures -- make the proposed estimators helpful for on-line time-saving characterization of a given PEMFC, and the implementation of fault-detection procedures and model-based adaptive control strategies. Simulation and experimental results that validate the theoretical claims are presented.

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arXiv2023

Synthesis of an adaptive observer of state variables for a linear stationary object in the presence of measurement noise

The article is devoted to the problem of synthesis of observers of state variables for linear stationary objects operating under conditions of noise or disturbances in the measurement channel. The paper considers a fully observable linear stationary system with known parameters. It is assumed that the state variables are not measured, and the measured output variable contains a small amplitude (in general, modulo less than one) additive noise or disturbance. It is also assumed that there is no a priori information about the disturbance or noise in the measurement channel (for example, frequency spectrum, covariance, etc.). It is well known that a large number of methods of observer synthesis have been obtained for this type of objects, including the Kalman filter, which has proven itself in practice. Under the condition of complete observability and the presence of some a priori information about the process (which is typical for the case when a disturbance in the measurement channel can be represented as white noise), approaches based on Kalman filtering demonstrate the highest quality of convergence of estimates of state variables to true values. Without taking into account the numerous results obtained using the application of the Kalman filter, an alternative idea of constructing an observer of state variables is considered in this paper. The alternative of the new approach is primarily due to the fact that there is no need to use the usual approaches based on the Luenberger observer. The paper proposes an approach based on the evaluation of unknown parameters (in this case, an unknown vector of initial conditions of the variables of the object state) of a linear regression model.

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arXiv2023

Adaptive observer of state variables of a nonlinear time varying system with unknown constant parameters

The paper proposes an adaptive observer of the state vector of a nonlinear time varying system based on measurements of the output variable. The problem is solved under the assumption that the control matrix (vector) and the nonlinear component of the equation of state of the system contain unknown constant parameters. When developing an adaptive observer, the GPEBO (generalized parameter estimation based observer) method was used, also known as a generalized observer based on parameter estimation, which was proposed in [1]. During the synthesis of the observer, a preliminary parametrization of the original nonlinear system is carried out. Then the resulting system is reduced to a linear regression model. At the next stage, unknown constant regression parameters are estimated using the least squares method with the forgetting factor [2, 3]. The article suggests the development of the result proposed by the authors in [4]. In [4], a linear non-stationary system containing unknown parameters in a control matrix (vector) was considered. This result is an extension of the result obtained in [4] for the case when the equation of state of the system contains a partially unknown nonlinearity.

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arXiv2023

A Globally Convergent Estimator of the Parameters of the Classical Model of a Continuous Stirred Tank Reactor

In this paper we provide the first solution to the challenging problem of designing a globally exponentially convergent estimator for the parameters of the standard model of a continuous stirred tank reactor. Because of the presence of non-separable exponential nonlinearities in the system dynamics that appear in Arrhenius law, none of the existing parameter estimators is able to deal with them in an efficient way and, in spite of many attempts, the problem was open for many years. To establish our result we propose a novel procedure to obtain a suitable nonlinearly parameterized regression equation and introduce a radically new estimation algorithm - derived applying the Immersion and Invariance methodology - that is applicable to these regression equations. A further contribution of the paper is that parameter convergence is guaranteed with weak excitation requirements.

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arXiv2022

Adaptive observer for a nonlinear system with partially unknown state matrix and delayed measurements

Problem of an adaptive state observer design for nonlinear system with unknown time-varying parameters and under condition of delayed measurements is considered. State observation problem was raised by many researchers (see for example Sanx et al. (2019)). In this paper the results proposed in Bobtsov et al. (2021b), Bobtsov et al. (2021a), Bobtsov et al. (2022a), Bobtsov et al. (2022b) are developed. The problem is solved under assumption that the state matrix can be represented as sum of known and unknown parts. The output vector is measured with a known constant delay. An adaptive observer which reconstructs unknown state and unknown time-varying parameter is proposed.

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arXiv2022

Parameter Estimation of Two Classes of Nonlinear Systems with Non-separable Nonlinear Parameterizations

In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical applications, and none of the existing parameter estimators is able to deal with them in an efficient way. The proposed estimation procedure is illustrated with two modern applications: fuel cells and human musculoskeletal dynamics. The procedure does not assume that the parameters live in known compact sets, that the nonlinearities satisfy some Lipschitzian properties, nor rely on injection of high-gain or the use of complex, computationally demanding methodologies. Instead, we propose to design a classical on-line estimator whose dynamics is described by an ordinary differential equation given in a compact precise form. A further contribution of the paper is the proof that parameter convergence is guaranteed with the extremely weak interval excitation requirement.

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arXiv2022

On-line Identification of Photovoltaic Arrays' Dynamic Model Parameters

This paper deals with the problem of on-line identification of the parameters of a realistic dynamical model of a photovoltaic array connected to a power system through a power converter. It has been shown in the literature that, when interacting with switching devices, this model is able to better account for the PV array operation, as compared to the classical five parameter static model of the array. While there are many results of identification of the parameters of the latter model, to the best of our knowledge, no one has provided a solution for the aforementioned more complex dynamic model since it concerns the parameter estimation of a nonlinear, underexcited system with unmeasurable state variables. Achieving such objective is the main contribution of the paper. We propose a new parameterisation of the dynamic model, which, combined with the powerful identification technique of dynamic regressor extension and mixing, ensures a fast and accurate online estimation of the unknown parameters. Realistic numerical examples via computer simulations are presented to assess the performance of the proposed approach -- even being able to track the parameter variations when the system changes operating point.

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arXiv2022

Adaptive observer for a LTV system with partially unknown state matrix and delayed measurements

Problem of adaptive state observer synthesis for linear time-varying (LTV) system with unknown time-varying parameter and delayed output measurements is considered. State observation problem has attracted the attention of many researchers $[4]$. In this paper the results proposed in the $[2]$, $[9]$, $[10]$ are developed. It is supposed that the state matrix can be represented as sum of known and unknown parts. Output vector is measured with known constant delay. An adaptive identification algorithm which reconstructs unknown state and unknown time varying parameter is proposed.

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