arXiv subjects

Konstantin Lastochkin

Publications and source records attributed to Konstantin Lastochkin.

At least 19 recordsLinked to original sources

arXiv2026

Estimation of Unknown Parameters in Presence of Perturbations and Noises with Application to GPEBO Design

A problem of online estimation of unknown parameters is considered for a linear regression equation, which is affected by an additive perturbation that can be caused by measurement noise (that corrupts regressor and regressand), as well as external perturbations. Known approaches to solve this problem typically have one of the following disadvantages: 1) they ensure convergence of a parametric error to a compact set with non-adjustable bound, 2) independence of all system regressor elements from the perturbation/noise is required to annihilate them, 3) an instrumental variable is needed to be selected. On the basis of the novel perturbation annihilation procedure, in the present paper, we propose three new estimation laws, which are free from the above-mentioned drawbacks and ensure exponential convergence of the parametric error to an arbitrarily small neighborhood of zero, particularly, in case more than a half (not all) of the regressor elements are independent from additive perturbation. One of the proposed estimation laws is used for the design of Generalized Parameter Estimation-Based Observer (GPEBO) for nonlinear affine systems to enhance GPEBO performance in case when the measured system output is corrupted by noise. The theoretical results are supported by examples and mathematical modelling.

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arXiv2024

Unbiased Parameter Estimation via DREM with Annihilators

In adaptive control theory, the dynamic regressor extension and mixing (DREM) procedure has become widespread as it allows one to describe major of adaptive control problems in unified terms of the parameter estimation problem of a regression equation with a scalar regressor. However, when the system/parameterization is affected by perturbations, the estimation laws, which are designed on the basis of such equation, asymptotically provides only biased estimates. In this paper, based on the bias-eliminated least-squares (BELS) approach, a modification of DREM procedure is proposed to annihilate perturbations asymptotically and, consequently, asymptotically obtain unbiased estimates. The theoretical results are supported with mathematical modelling and can be used to design adaptive observers and control systems.

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arXiv2024

Composite Adaptive Disturbance Rejection in Robotics via Instrumental Variables based DREM

In this paper we consider trajectory tracking problem for robotic systems affected by unknown external perturbations. Considering possible solutions, we restrict our attention to composite adaptation, which, particularly, ensures parametric error convergence being desirable to enhance overall stability and robustness of a closed-loop system. At the same time, existing composite approaches cannot simultaneously relax stringent persistence of excitation requirement and guarantee convergence of parametric error to zero for a perturbed scenario. So, a new composite adaptation scheme is proposed, which successfully overcomes mentioned problems of known counterparts and has several salient features. First, it includes a novel adaptive disturbance rejection control law for a general n-DoF dynamical model in the Euler-Lagrange form, which, without achievement of the parameter estimation goal, ensures global stability via application of a high-gain external torque observer augmented with some adaptation law. Secondly, such law is extended with a composite summand derived via the recently proposed Instrumental Variables based Dynamic Regressor Extension and Mixing procedure, which relaxes excitation conditions and ensures asymptotic parameter estimation and reference tracking in the presence of external torque under some non-restrictive assumptions. An illustrative example shows the effectiveness and superiority of the proposed approach in comparison with existing solutions.

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arXiv2024

Instrumental Variables based DREM for Online Asymptotic Identification of Perturbed Linear Systems

Existing online continuous-time parameter estimation laws provide exact (asymptotic/exponential or finite/fixed time) identification of dynamical linear/nonlinear systems parameters only if the external perturbations are equaled to zero or independent with the regressor of the system. However, in real systems the disturbances are almost always non-vanishing and dependent with the regressor. In the presence of perturbations with such properties the above-mentioned identification approaches ensure only boundedness of a parameter estimation error. The main goal of this study is to close this gap and develop a novel online continuous-time parameter estimator, which guarantees exact asymptotic identification of unknown parameters of linear systems in the presence of unknown but bounded perturbations and has relaxed convergence conditions. To achieve the aforementioned goal, it is proposed to augment the deeply investigated Dynamic Regressor Extension and Mixing (DREM) procedure with the novel Instrumental Variables (IV) based extension scheme with averaging. Such an approach allows one to obtain a set of scalar regression equations with asymptotically vanishing perturbation if the initial disturbance that affects the plant is bounded and independent not with the system regressor, but with the instrumental variable. It is rigorously proved that a gradient estimation law designed on the basis of such scalar regressions ensures online unbiased asymptotic identification of the parameters of the perturbed linear systems if some weak independence and excitation assumptions are met. Theoretical results are illustrated and supported with adequate numerical simulations.

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arXiv2024

Adaptive Reconstruction of Nonlinear Systems States via DREM with Perturbation Annihilation

A new adaptive observer is proposed for a certain class of nonlinear systems with bounded unknown input and parametric uncertainty. Unlike most existing solutions, the proposed approach ensures asymptotic convergence of the unknown parameters, state and perturbation estimates to an arbitrarily small neighborhood of the equilibrium point. The solution is based on the novel augmentation of a high-gain observer with the dynamic regressor extension and mixing (DREM) procedure enhanced with a perturbation annihilation algorithm. The aforementioned properties of the proposed solution are verified via numerical experiments.

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arXiv2024

Parameter Estimation-Based States Reconstruction of Uncertain Linear Systems with Overparameterization and Unknown Additive Perturbations

The problem of state reconstruction is considered for uncertain linear time-invariant systems with overparameterization, arbitrary state-space matrices and unknown additive perturbation described by an exosystem. A novel adaptive observer is proposed to solve it, which, unlike known solutions, simultaneously: (i) reconstructs the physical state of the original system rather than the virtual state of its observer canonical form, (ii) ensures exponential convergence of the reconstruction error to zero when the condition of finite excitation is satisfied, (iii) is applicable to systems, in which mentioned perturbation is generated by an exosystem with fully uncertain constant parameters. The proposed solution uses a recently published parametrization of uncertain linear systems with unknown additive perturbations, the dynamic regressor extension and mixing procedure, as well as a method of physical states reconstruction developed by the authors. Detailed analysis for stability and convergence has been provided along with simulation results to validate the theoretical analysis.

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arXiv2024

Parameter Estimation-Based Extended Observer for Linear Systems with Polynomial Overparameterization

We consider a class of uncertain linear time-invariant overparametrized systems affected by bounded disturbances, which are described by a known exosystem with unknown initial conditions. For such systems an exponentially stable extended adaptive observer is proposed, which, unlike existing solutions, simultaneously: (i) allows one to reconstruct original (physical) states of the system represented in arbitrarily chosen state-space form rather than virtual states of the observer canonical form; (ii) ensures convergence of the state observation error to zero under weak requirement of the regressor finite excitation; (iii) does not include Luenberger correction gain and forms states estimate using algebraic rather than differential equation; (iv) additionally reconstructs the unmeasured external disturbance. The proposed solution is based on the new parametrizations to identify the observer parameters obtained with the help of the heterogeneous mappings and the dynamic regressor extension and mixing procedure. Illustrative simulations support obtained theoretical results.

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arXiv2024

Exact Asymptotic Estimation of Unknown Parameters of Perturbed LRE with Application to State Observation

Most identification laws of unknown parameters of linear regression equations (LRE) ensure only boundedness of a parametric error in the presence of additive perturbations, which is almost always unacceptable for practical scenarios. In this paper, a new identification law is proposed to overcome this drawback and guarantee asymptotic convergence of the unknown parameters estimation error to zero in case the mentioned additive perturbation meets special averaging conditions. Such law is successfully applied to state reconstruction problem. Theoretical results are illustrated by numerical simulations.

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arXiv2023

Exponentially Stable Adaptive Optimal Control of Uncertain LTI Systems

A novel method of an adaptive linear quadratic (LQ) regulation of uncertain continuous linear time-invariant systems is proposed. Such an approach is based on the direct self-tuning regulators design framework and the exponentially stable adaptive control technique developed earlier by the authors. Unlike the known solutions, a procedure is proposed to obtain a non-overparametrized regression equation (RE) with respect to the unknown controller parameters from an initial RE of the LQ-based reference tracking control system. On the basis of such result, an adaptive law is proposed, which under mild regressor finite excitation condition provides monotonous convergence of the LQ-controller parameters to an adjustable set of their true values, which bound is defined only by the machine precision. Using the Lyapunov-based analysis, it is proved that the mentioned law guarantees the exponential stability of the closed-loop adaptive optimal control system. The simulation examples are provided to validate the theoretical contributions.

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arXiv2023

Exponentially Stable Adaptive Observation for Systems Parameterized by Unknown Physical Parameters

The method to design exponentially stable adaptive observers is proposed for linear time-invariant systems parameterized by unknown physical parameters. Unlike existing adaptive solutions, the system state-space matrices A, B are not restricted to be represented in the observer canonical form to implement the observer. The original system description is used instead, and, consequently, the original state vector is obtained. The class of systems for which the method is applicable is identified via three assumptions related to: (i) the boundedness of a control signal and all system trajectories, (ii) the identifiability of the physical parameters of A and B from the numerator and denominator polynomials of a system input/output transfer function and (iii) the complete observability of system states. In case they are met and the regressor is finitely exciting, the proposed adaptive observer, which is based on the known GPEBO and DREM procedures, ensures exponential convergence of both system parameters and states estimates to their true values. Detailed analysis for stability and convergence has been provided along with simulation results to validate the developed theory.

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arXiv2023

Monotonous Parameter Estimation of One Class of Nonlinearly Parameterized Regressions without Overparameterization

The estimation law of unknown parameters vector $θ$ is proposed for one class of nonlinearly parametrized regression equations $y\left( t \right) = Ω\left( t \right)Θ\left( θ\right)$. We restrict our attention to parametrizations that are widely obtained in practical scenarios when polynomials in $θ$ are used to form $Θ\left( θ\right)$. For them we introduce a new 'linearizability' assumption that a mapping from overparametrized vector of parameters $Θ\left( θ\right)$ to original one $θ$ exists in terms of standard algebraic functions. Under such assumption and weak requirement of the regressor finite excitation, on the basis of dynamic regressor extension and mixing technique we propose a procedure to reduce the nonlinear regression equation to the linear parameterization without application of singularity causing operations and the need to identify the overparametrized parameters vector. As a result, an estimation law with exponential convergence rate is derived, which, unlike known solutions, (i) does not require a strict P-monotonicity condition to be met and a priori information about $θ$ to be known, (ii) ensures elementwise monotonicity for the parameter error vector. The effectiveness of our approach is illustrated with both academic example and 2-DOF robot manipulator control problem.

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arXiv2023

Exponentially Stable Adaptive Control of MIMO Systems with Unknown Control Matrix

The scope of this research is a problem of the direct model reference adaptive control of linear time-invariant multi-input multi-output (MIMO) plants without any a priori knowledge about system matrices. To handle it, a new method is proposed, which includes three main stages. Firstly, using the well-known DREM procedure, the plant parametrization is made to obtain the linear regressions, in which the plant matrices and state initial conditions are the unknown parameters. Secondly, such regressions are substituted into the known equations for the controller parameters calculation. Thirdly, the controller parameters are identified using the novel adjustment law with exponential rate of convergence. To the best of the authors knowledge, such a method is the first one to provide the following features simultaneously: 1) it is applicable for the generic completely unknown MIMO systems (e.g. without any information about state or control allocation matrices, the sign of the latter, etc.); 2) it guarantees the exponential convergence of both the parameter and tracking errors under the mild requirement of the regressor finite excitation; 3) it ensures monotonicity of the transient curves of the control law parameters matrices. The results of the conducted experiments with the model of a rubber and ailerons control of a small passenger aircraft corroborate all the theoretical results.

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arXiv2023

Sensorless Adaptive Vibration Suppression in Two-Mass Systems via Joint Estimation of Controller Parameters and System States

The scope of this study is to develop a novel sensorless adaptive vibration suppression controller for two-mass systems with joint estimation of states and controller parameters. Unlike existing solutions, we simultaneously: (i) propose an analytically proved, unified and singularity-issue-free scheme of parameters adjustment of a control law with additional feedbacks that ensures convergence of such parameters to their true values under extremely weak regressor finite excitation (FE) requirement, (ii) derive an adaptive observer of a two-mass electromechanical system physical states with guarantee of their convergence to the ground truth values under clear FE condition, (iii) rigorously prove the exponential stability of the obtained closed-loop system of adaptive vibration suppression for two-mass systems that includes the above-mentioned adaptive observer and adaptive controller. These approaches are grounded on the recently proposed method of parameters identification for one class of nonlinearly parameterized regression equation and thoroughly investigated dynamic regression extension and mixing procedure (DREM). The obtained theoretical results are confirmed via numerical experiments.

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arXiv2023

Extended Adaptive Observer for Linear Systems with Overparametrization

Exponentially stable extended adaptive observer is proposed for a class of linear time-invariant systems with unknown parameters and overparameterization. It allows one to reconstruct unmeasured states and bounded external disturbance produced by a known linear exosystem with unknown initial conditions if a weak requirement of regressor finite excitation is met. In contrast to the existing solutions, the proposed observer reconstructs the original (physical) states of the system rather than the virtual one of its observer canonical form. Simulation results to validate the developed theory are presented.

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arXiv2023

Parameter Estimation-Based Observer for Linear Systems with Polynomial Overparametrization

An adaptive state observer is proposed for a class of overparametrized uncertain linear time-invariant systems without restrictive requirement of their representation in the observer canonical form. It evolves the method of generalized parameters estimation-based observer design and, therefore, (i) does not require to identify Luenberger correction gain parameters, (ii) forms states using algebraic rather than differential equation. Additionally, the developed observer is applicable to systems with unknown output matrix and ensures exponential convergence of unmeasured state observation error under weak requirement of the regressor finite excitation. The effectiveness of the proposed solution is supported by simulation results.

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arXiv2022

Exponentially Stable Adaptive Control Under Semi-PE Condition

A novel method of exponentially stable adaptive control to compensate for matched parametric uncertainty under a mild condition of semi-persistent excitation (s-PE) of a regressor with piecewise-constant rank and nullspace is proposed. It is based on the generalized dynamic regressor extension and mixing procedure developed earlier by the authors, does not require high adaptive gain or data stacks and ensures: 1) exponential convergence of the tracking error to zero and the parameter one to a bounded set when the regressor is s-PE, 2) adjustable parameters transients of first-order type (each scalar parameter is adjusted using a separate first-order scalar differential equation), 3) alertness to change of the uncertainty parameters values, and 4) boundedness of all signals when the regressor is not s-PE. The main salient feature of the proposed approach is that the exponential stability is guaranteed when the controller parameters estimates converge to the values that are indistinguishable from the true ones. The results of numerical experiments fully support the theoretical analysis and demonstrate the advantages of the proposed method.

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arXiv2022

Regression Filtration with Resetting to Provide Exponential Convergence of MRAC for Plants with Jump Change of Unknown Parameters

This paper proposes a new method to provide the exponential convergence of both the parameter and tracking errors of the composite adaptive control system without the persistent excitation (PE) requirement. Instead, the derived composite adaptive law ensures the above-mentioned properties under the strictly weaker finite excitation (FE) condition. Unlike known solutions, in addition to the PE requirement relaxation, it provides better transient response under jump change of the plant uncertainty parameters. To derive such an adaptive law, a novel scheme of uncertainty filtration with resetting is proposed, which provides the required properties of the control system. A rigorous proof of all mentioned properties of the developed adaptive law is presented. Such law is compared with the known composite ones, which also relax the PE requirement, using the wing-rock problem to conduct numerical experiments. The obtained results fully support the theoretical analysis and demonstrate the advantages of the proposed method.

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arXiv2022

Relaxation of Conditions for Convergence of Dynamic Regressor Extension and Mixing Procedure

A generalization of the dynamic regressor extension and mixing procedure is proposed, which, unlike the original procedure, first, guarantees a reduction of the unknown parameter identification error if the requirement of regressor semi-finite excitation is met, and second, it ensures exponential convergence of the regression function (regressand) tracking error to zero when the regressor is semi-persistently exciting with a rank one or higher.

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