Denis Efimov

National Institute for Research in Computer Science and Control | INRIA · Valse Team

In this paper, we propose the design of a robust control strategy for the trajectory tracking problem in perturbed unicycle mobile robots. The proposed strategy comprises the design of a robust control law, which is based on an Integral Sliding-Mode Control (ISMC) approach together with an interval predictor-based state-feedback controller through...

For a second‐order system with vector position, either constant or time‐varying delays, and a power nonlinearity of the degree higher than one, which does not contain a velocity‐proportional damping term, the conditions of local input‐to‐state stability are proposed. The result is based on application of Lyapunov‐Razumikhin approach, for which new...

A simple fixed-time converging estimation algorithm is presented for a linear regression using the dynamic regressor extension and mixing (DREM) method within a discrete-time setting, with a persistently excited regressor and bounded measurement noises. The solution is based on Kreisselmeier's filters, and it is computationally simpler than the exi...

The problems of interval estimation and stabilization are studied for a class of generalized Persidskii systems. For this class of models with nonlinearities satisfying the incremental passivity property, the nonnegativity conditions are proposed and a nonlinear interval observer is synthesized. A nonlinear feedback is designed that uses the interv...

We propose an adaptive observer for a class of nonlinear time-varying systems, for which the regressor depends not only on the known input-output signals but also on all the unmeasured states. There are state disturbances, and measurements are corrupted by noise. The Lyapunov function method is used to prove that the coupled system-observer dynamic...

This article deals with the problem of time-varying parameter identification in dynamical regression models affected by disturbances. The disturbances comprise time-dependent external perturbations and nonlinear unmodeled dynamics. With this aim in mind, we propose a robust nonlinear adaptive observer. The algorithm ensures the asymptotic convergen...

The problem of finite-time stabilization of a linear plant with an optimization of both a settling time and an averaged/weighted control energy is studied using the concept of generalized homogeneity. It is shown that the optimal finite-time stabilizing control in this case can be designed by means of solving a simple linear algebraic equation. Rob...

We present new results for the analysis of global boundedness of state periodic systems. Thereby, we address both the case of systems, whose dynamics is periodic with respect to a part of the state vector and the case of systems, whose dynamics is periodic with respect to all state variables. To derive the results the notion of strong Leonov...

In this paper, the effect of a homogeneous parasitic dynamics on the stability of a homogeneous system, when homogeneity degrees are possibly different, is studied via ISS approach in the framework of singular perturbations. Thus, the possibilities to reduce the order of the interconnected system considering only the reduced-order dynamics and negl...

In this chapter, we propose an explicit discretization scheme for class of disturbed systems controlled by homogeneous quasi-continuous high-order sliding-mode controllers which are equipped with a homogeneous Lyapunov function. Such a Lyapunov function is used to construct the discretization scheme that preserves important features from the origin...

This paper presents the design of a robust controller, based on an integral sliding–mode control (ISMC) approach together with an interval predictor–based state feedback controller and a Model Predictive Control (MPC) scheme, for a class of uncertain linear parameter-varying (LPV) systems. The proposed controller deals with some state and input con...

In this paper, we design a robust control strategy to solve the trajectory-tracking problem for perturbed unicycle mobile robots. The design is composed of an Integral Sliding-Mode Control, an interval predictor-based state-feedback controller and a Model Predictive Control. The controller handles some perturbations in the kinematic model, and stat...

In this paper a solution for the stabilization problem is proposed for continuous-time nonlinear systems, taking into account state and input constraints. The proposed sampled-time controller includes the design of a control law based on an interval predictor-based state-feedback controller and a model predictive control (MPC) approach that deals w...

This paper contributes to the design of a robust control strategy for the trajectory tracking problem in perturbed unicycle mobile robots. The proposed strategy comprises the design of a robust control law, which is based on an Integral Sliding–Mode Control (ISMC) approach together with an interval predictor–based state–feedback controller and a Mo...

This paper proposes the design of a robust sampled–time controller to stabilize continuous–time nonlinear systems, taking into account state and input constraints. The proposed controller comprises the design of a robust control law, which is based on an interval predictor–based state–feedback controller and a Model Predictive Control (MPC) approac...

This paper presents the design of a robust control strategy for linear parameter–varying (LPV) systems. The proposed strategy involves the design of a robust control law based on an integral sliding–mode control (ISMC) approach with an interval predictor–based state feedback controller and a Model Predictive Control (MPC) scheme. The proposed contr...

In this paper, we study the problem of robust stabilization of affine nonlinear multistable systems in the presence of exogenous disturbances. The results are based on the theory of input‐to‐state stability (ISS) and integral input‐to‐state stability (iISS) for systems with multiple invariant sets. The notions of ISS and iISS control Lyapunov funct...

Integrating renewable energy sources into an unbalanced distribution network requires fast and accurate extraction of fundamental frequency positive‐ and negative‐sequence components from the unbalanced three‐phase grid voltage signals. For this purpose, various methods are already available in the literature. Out of them, delayed signal cancellati...

In this paper, an approach is proposed for the remote observation of a dynamical system through a data-rate constrained communication channel. The focus is put on discrete-time systems with a Lipschitz nonlinearity, driven by an external signal, and subject to bounded state perturbation and measurement error. The problem at hand is providing estima...

This paper considers the state estimation problem for a class of non-autonomous nonlinear systems. We propose conditions on the existence and stability of a nonlinear observer based on the invariant manifold approach in both continuous- and discrete-time scenarios. The requirements are formulated using Linear Matrix Equalities (LME) and Inequalitie...

For input-affine nonlinear dynamical systems, an input-to-state stability analysis with respect to (weighted) average values of exogenous perturbations is proposed. The time-delay method is used to represent the system in a suitable form for investigation: a kind of neutral-type differential equation. The introduced approach allows the asymptotic g...

For a canonical form of mechanical systems defined through gradients of potential energy and dissipative terms, the conditions of finite-time and fixed-time (integral) input-to-state stability are derived by finding suitable Lyapunov functions. The proposed stability conditions are constructive, which is demonstrated in several applications.

For two canonical models of mechanical systems with disturbances presented by Rayleigh‐ and Liénard‐type equations, several designs of Lyapunov functions are investigated. Under given restrictions, the existence of these functions implies global or local input‐to‐state stability property for the systems. The proposed stability conditions are constr...

Industrial control systems have been frequent targets of cyber attacks during the last decade. Adversaries can hinder the safe operation of these systems by tampering with their sensors and actuators, while ensuring that the monitoring systems are not able to detect such attacks in time. This paper presents methods to design and overcome stealthy a...

In this paper, an event-triggered observation scheme is considered for a perturbed nonlinear dynamical system connected to a remote location via a communication channel, which can only transmit a limited amount of data per unit of time. The dynamical system, which is supposed to be globally Lipschitz, is subject to bounded state perturbations. More...

This article studies the problem of fundamental frequency positive-sequence component separation in unbalanced three-phase systems for grid-integration applications. We propose a-simple-to-implement approach involving a modified delayed signal cancellation method and moving average filtering. A delay-based linear-regression framework is considered...

In this paper, a robust adaptive observer is proposed for dynamical disturbed regression models. For the constant unknown parameters case, the proposed algorithm ensures asymptotic convergence to zero of the parameter identification error in presence of time-dependent external disturbances. For the case of the time-varying parameters, the parameter...

In this paper, a robust control strategy for a QuadRotor, under the effect of external disturbances, is proposed to track a movil target, considering time delayed measurements of the target position. For the target position, it is assumed that a monocular camera is fixed in the center of the QuadRotors bottom. It is considered that the frame rate o...

In this article, we address the problem of adaptive state observation of linear time‐varying systems with delayed measurements and unknown parameters. Our new developments extend the results reported in our recently works. The case with known parameters has been studied by many researchers. However in this article we show that the generalized param...

The dynamic regressor extension and mixing (DREM) method provides a fixed-time converging parameter estimator for a persistently excited regressor under bounded measurement noises. This note aims to develop this approach for cases with weaker excitation and regressor constraints. Several nonlinear estimation schemes with fixed-time convergence rate...

The concept of practical fixed-time input-to-state stability for neutral time-delay systems with exogenous perturbations is introduced. Lyapunov–Krasovskii theorems are formulated in explicit and implicit ways. Further, the problem of static nonlinear output-feedback stabilization of a linear system with parametric uncertainties, external bounded s...

A mechanical system under strongly nonlinear potential and dissipative forces, with nonlinear nonstationary perturbations having zero mean values, is studied. Proposing a special construction of Lyapunov function, the conditions are found, under which the perturbations do not influence the asymptotic stability of the trivial equilibrium position of...

The problem of finite‐time and fixed‐time stability analysis is considered for a class of nonlinear systems x˙=H(x)b(x),$$ \dot{x}=H(x)b(x), $$ where H$$ H $$ is homogeneous of a degree ν≠0$$ \nu \ne 0 $$ and b$$ b $$ is bounded. It is shown that under certain conditions on b$$ b $$ the asymptotic stability of the system implies its finite‐time sta...

A state observer is designed for a class of generalized Persidskii systems with nonlinear measurements, state disturbances, and output noise. We assume that all nonlinearities are diagonal and belong to a sector. The robust stability and convergence conditions for the estimation error are obtained by applying the theory of input-to-output stability...

Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure is formalized in LMI form. Through numeric experiments, it is observed that the proposed hyperexponential contr...

The paper proposes an algorithm for a discretization (sampled-time implementation) of a homogeneous control preserving the finite-time and nearly fixed-time stability property of the original (sampling-free) system. The sampling period is assumed to be constant. Both single-input and multiple-input cases are considered. The robustness (Input-to-Sta...

The article is devoted to the problem of finite‐time and fixed‐time observation of linear multiple input multiple output control systems. The proposed dynamic observers do not require system transformation to a canonical form and guarantee convergence of the observation error to zero in a finite or in a fixed time. It is shown that the observers ar...

The problem of delay-independent stability is studied for a class of mechanical systems under dissipative, non-conservative and potential forces, which are described by homogeneous terms. The obtained conditions are extended to the case of switched force model under arbitrary and restricted commutation laws. The proof is based on analysis of a comp...

A grid-synchronization-based fundamental frequency positive-sequence (FFPS) and negative-sequence (FFNS) amplitudes estimation technique is proposed for unbalanced and distorted grid. In this technique, the sequence amplitudes are extracted by extracting the phase-angle of the FFPS and FFNS components. The extracted phase-angles have DC and double...

Delayed signal cancellation (DSC) is a popular method to separate the fundamental frequency positive- and negative-sequence components from unbalanced three-phase signals. Conventional DSC can separate the sequence components using a quarter-cycle delay. Fast DSC tools can achieve the same with less than a quarter-cycle delay. However, neither conv...

This paper introduces the notions of annular settling and output annular settling for general nonlinear systems. Also, we propose conditions for annular short-time stability, short time boundedness with a nonzero initial state, annular settling, and output annular settling for generalized Persidskii systems with an essentially bounded input. These...

The present article provides a sufficient condition to ensure output finite‐time and fixed‐time stability. Comparing with analogous researches the proposed result is less restrictive and obtained for a wider class of systems. The presented output stability condition is used for adaptive control design, where the state vector of a plant is extended...

Parametric estimation of a biased harmonic signal is a significant technical challenge for many engineering applications. Such a problem is particularly important for electric utility grid-connected power electronic converters. This article utilizes a linear regression model of the signal to solve this interesting practical problem. A continuous-ti...

Razumikhin-like theorems on hyperexponential and fixed-time stability of time-delay systems are proposed for both explicitly and implicitly defined Lyapunov functions. While the former method is useful for stability analysis, the latter approach is more suitable for control synthesis. Examples of systems that can be stabilized hyperexponentially an...

In this paper we address the problem of adaptive state observation of affine-in-the-states time-varying systems with delayed measurements and unknown parameters. The development of the results proposed in the [Bobtsov et al. 2021a] and in the [Bobtsov et al. 2021c] is considered. The case with known parameters has been studied by many researchers—s...

In this paper, input-to-state stability and stabilization conditions in time-delay generalized Persidskii systems are studied. These conditions are formulated in terms of linear matrix inequalities, which may depend on delay values, and be local or global in state space. Numerical examples of opinion dynamics and the Lotka-Volterra model illustrate...

A high-order sliding-mode adaptive observer is proposed to solve the problem of adaptive estimation, i.e., the simultaneous estimation of the state and parameters, for a class of uncertain nonlinear systems in the presence of external disturbances, that does not need to satisfy a relative degree condition equal to one. This approach is based on a h...

This article proposes a new simplified pointing model as a feedback-based dynamical system, including both human and computer sides of the process. It takes into account the commutation between the correction and ballistic phases in pointing tasks. We use the mouse position increment signal from noisy experimental data to achieve our main objective...

In this article, the problem of state estimation of a microbial consortium is discussed. This microbial consortium is composed of two strains, called producer and cleaner, in continuous culture. The producer strain grows by consuming glucose, while the cleaner grows by consuming the acetate excreted by the producer and toxifies the environment. Con...

In this paper we address the problem of adaptive state observation of affine-inthe-states time-varying systems with delayed measurements and unknown parameters. The development of the results proposed in the [Bobtsov et al. 2021a] and in the [Bobtsov et al. 2021c] is considered. The case with known parameters has been studied by many researchers (s...

The conditions of (integral) input-to-state stability and input–output-to-state stability are established for a class of generalized Persidskii systems. The proposed conditions are formulated using linear matrix inequalities. Based on these results the conditions of convergence are derived for discretizations of this class of models obtained by the...

In this work, stability analysis for a class of switched nonlinear time-delay systems is performed by applying Lyapunov–Krasovskii and Lyapunov–Razumikhin approaches. It is assumed that each subsystem in the family is homogeneous (of positive or negative degree) and asymptotically stable in the delay-free setting. The cases of existence of a common...

This work addresses the problem of robust output feedback model predictive control (MPC) of constrained, discrete‐time, time‐delayed linear systems subject to (bounded) additive disturbances. The proposed predictive controller incorporates an interval observer, that exploits the available measurement to update the set‐membership of the system state...