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Denis Efimov

Publications and source records attributed to Denis Efimov.

At least 19 recordsLinked to original sources

Robust Fixed-Time Model Reference Adaptive Control

This article proposes a Model Reference Adaptive Control (MRAC) strategy to achieve fixed-time convergence of parameter estimation and tracking errors for unknown linear time-invariant systems, without relying on the persistence of excitation condition. Instead, it employs a less restrictive initial/interval excitation condition on the regressor matrix, enhancing practicality and ease of implementation in real-world scenarios. Our primary contribution is a novel parameter update law within the indirect MRAC framework, ensuring that parameter estimates converge within a fixed time, once the initial/interval excitation condition is met. This approach simplifies the practical requirements for adaptive control while guaranteeing robust performance against parameter uncertainty and external disturbances. Simulation results provide a comparison with the current literature to validate the effectiveness of this approach.

eess.SY

Accelerated Stabilization of Switched Linear MIMO Systems using Generalized Homogeneity

This paper addresses the problem of exponential and accelerated finite-time, as well as nearly fixed-time, stabilization of switched linear MIMO systems. The proposed approach relies on a generalized homogenization framework for switched linear systems and employs implicit Lyapunov functions for control design, covering both common and multiple Lyapunov function settings. Linear matrix equations and inequalities are derived to characterize the dilation generator and to synthesize the controller gains. Robustness of the resulting control laws with respect to system uncertainties and external disturbances is analyzed. The effectiveness of the proposed approach is illustrated through numerical examples.

eess.SY

Robustness of Delayed Higher Order Sliding Mode Control

In this paper, the feasibility of recently developed higher order delayed sliding mode controllers is addressed. With this aim the robustness against the measurement noise and mismatched perturbations for the systems governed by such controllers is established using ISS implicit Lyapunov-Razumikhin function approach. To illustrate proposed results, a simulation example validating the efficiency of the method is provided.

eess.SY

Modified global finite-time quasi-continuous second-order robust feedback control

A non-overshooting quasi-continuous sliding mode control with sub-optimal damping was recently introduced in Ruderman and Efimov (2025) for perturbed second-order systems. The present work proposes an essential modification of the nonlinear control law which (i) allows for a parameterizable control amplitude limitation in a large subset of the initial values, (ii) admits an entire state-space R2 (that was not given in Ruderman and Efimov (2025)) for the finite-time control, and finally (iii) enables for the found analytic solution of the state trajectories in the unperturbed case. The latter allows also for an exact estimation of the finite convergence time, and open an avenue for other potentially interesting analysis of the control properties in the future. For a perturbed case, the solution-based and Lyapunov function-based approaches are developed to show the uniform global asymptotic stability. The proposed robustness and convergence analysis are accompanied by several illustrative numerical examples.

math.OC

On hyperexponential stabilization of a chain of integrators in continuous and discrete time subject to unmatched perturbations

A recursive time-varying state feedback is presented for a chain of integrators with unmatched perturbations in continuous and discrete time. In continuous time, it is shown that hyperexponential convergence is achieved for the first state variable \(x_1\), while the second state \(x_2\) remains bounded. For the other states, we establish ISS {\cb property} by saturating the growing {\cb control} gain. In discrete time, we use implicit Euler discretization to {\cb preserve} hyperexponential convergence. The main results are demonstrated through several examples of the proposed control laws, illustrating the conditions established for both continuous and discrete-time systems.

eess.SY

Regularization of non-overshooting quasi-continuous sliding mode control for chattering suppression at equilibrium

Robust finite-time feedback controller introduced for the second-order systems in [1] can be seen as a non-overshooting quasi-continuous sliding mode control. The paper proposes a regularization scheme to suppress inherent chattering due to discontinuity of the control [1] in the origin, in favor of practical applications. A detailed analysis with ISS and iISS proofs are provided along with supporting numerical results.

math.OC

Power-based control of output oscillations with online estimation of biased harmonics

The recently introduced discrete power-based control (Ruderman (2024b)) reduces largely the communication efforts in the control loop when compensating for the marginally damped or even slowly diverging output oscillations. The control commutates twice per oscillations period (at the amplitude peaks) and uses the measured harmonic output only. The power-based control scheme requires the knowledge of the instantaneous frequency, amplitude, and bias parameters of the harmonic signal. This paper extends the power-based control by the finite-time estimation of the biased harmonics (Ahmed et al. (2022)). Also an improved analytic calculation of the impulse weighting factor is provided. The power-based oscillations control with online estimation of the harmonic parameters is evaluated experimentally on the fifth-order actuator system with a free hanging load under gravity and measurement noise.

eess.SY

Open-loop control design for contraction in affine nonlinear systems

In this paper, first, it is shown that if a nonlinear time-varying system is contractive, then it is incrementally exponentially stable. Second, leveraging this result, under mild restrictions, an approach is proposed to design feedforward inputs for affine in control systems providing contraction/incremental exponential stability. Unlike standard stability notions, which have well-established control design techniques, this note can be considered among the first ones to provide such a tool for a kind of incremental stability. The theoretical findings are illustrated by examples.

eess.SY

Small-gain conditions for exponential incremental stability in feedback interconnections

We prove that under a small-gain condition, an interconnection of two globally incrementally exponentially stable systems inherits this property on any compact connected forward invariant set. It is also demonstrated that the interconnection inherits a weaker version of incremental exponential stability globally. An example illustrating the theoretical findings is given. The example also shows that the uniform negativity of the Jacobian is not necessary for incremental exponential stability.

eess.SY

Non-overshooting continuous in convergence sliding mode control of second-order systems

This paper proposes a novel nonlinear sliding mode state feedback controller for perturbed second-order systems. In analogy to a linear proportional-derivative (PD) feedback control, the proposed nonlinear scheme uses the output of interest and its time derivative. The control has only one free design parameter, and the closed-loop system is shown to possess uniform boundedness and finite-time convergence of trajectories in the presence of matched disturbances. We derive a strict Lyapunov function for the closed-loop control system with a bounded exogenous perturbation, and use it for both, the control parameter tuning and analysis of the finite-time convergence. The essential features of the proposed new control law is non-overshooting despite the unknown dynamic disturbances and the continuous control action during the convergence to zero equilibrium. Apart from the numerical results, a revealing experimental example is also shown in favor of the proposed control and in comparison with PD and sub-optimal nonlinear damping regulators.

math.OC

Filtering Homogeneous Observer for MIMO System

Homogeneous observer for linear multi-input multi-output (MIMO) system is designed. A prefilter of the output is utilized in order to improve robustness of the observer with respect to measurement noises. The use of such a prefilter also simplifies tuning, since the observer gains in this case are parameterized by a linear matrix inequality (LMI) being always feasible for observable system. In particular case, the observer is shown to be applicable in the presence of the state and the output bounded perturbations. Theoretical results are supported by numerical simulations.

eess.SY

Learning linear dynamical systems under convex constraints

We consider the problem of finite-time identification of linear dynamical systems from $T$ samples of a single trajectory. Recent results have predominantly focused on the setup where either no structural assumption is made on the system matrix $A^* \in \mathbb{R}^{n \times n}$, or specific structural assumptions (e.g. sparsity) are made on $A^*$. We assume prior structural information on $A^*$ is available, which can be captured in the form of a convex set $\mathcal{K}$ containing $A^*$. For the solution of the ensuing constrained least squares estimator, we derive non-asymptotic error bounds in the Frobenius norm that depend on the local size of $\mathcal{K}$ at $A^*$. To illustrate the usefulness of these results, we instantiate them for four examples, namely when (i) $A^*$ is sparse and $\mathcal{K}$ is a suitably scaled $\ell_1$ ball; (ii) $\mathcal{K}$ is a subspace; (iii) $\mathcal{K}$ consists of matrices each of which is formed by sampling a bivariate convex function on a uniform $n \times n$ grid (convex regression); (iv) $\mathcal{K}$ consists of matrices each row of which is formed by uniform sampling (with step size $1/T$) of a univariate Lipschitz function. In all these situations, we show that $A^*$ can be reliably estimated for values of $T$ much smaller than what is needed for the unconstrained setting.

math.ST

Stability analysis and stabilization of systems with hyperexponential rates

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 control is less sensitive with respect to noises and discretization errors than its finite-time analog. It also demonstrates better performance in the presence of delays as well. Theoretical results are supported by numerical simulations.

eess.SY

Consistent discretization of finite/fixed-time controllers

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-State Stability) of the obtained sampled-time control system is studied as well. Theoretical results are supported by numerical simulations.

eess.SY

On annular short-time stability conditions for generalized Persidskii systems

This paper studies the trajectory behavior evaluation for generalized Persidskii systems with an essentially bounded input on a finite time interval. Also, the notions of annular settling and output annular settling for general nonlinear systems are introduced. We propose conditions for annular short-time stability, short-time boundedness with a nonzero initial state, annular settling, and output annular settling for a class of Persidskii systems. These conditions are based on the verification of linear matrix inequalities. An application to recurrent neural networks illustrates the usefulness of the proposed notions and conditions.

eess.SY

State Observation of Affine-in-the-States Systems with Unknown Time-Varying Parameters and Output Delay

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 (see [Sanz et al. 2019, Bobtsov et al. 2021b] and references therein) where, similarly to the approach adopted here, the system is treated as a linear time-varying system. We show that the parameter estimation-based observer (PEBO) design proposed in [Ortega et al. 2015, 2021] provides a very simple solution for the unknown parameter case. Moreover, when PEBO is combined with the dynamic regressor extension and mixing (DREM) estimation technique [Aranovskiy et al. 2016, Ortega et al. 2019], the estimated state converges in fixed-time with extremely weak excitation assumptions.

math.OC

Adaptive Finite-time and Fixed-time Control Design using Output Stability Conditions

The present paper 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 by adjustable control parameters.

math.OC

Robust-Adaptive Control of Linear Systems: beyond Quadratic Costs

We consider the problem of robust and adaptive model predictive control (MPC) of a linear system, with unknown parameters that are learned along the way (adaptive), in a critical setting where failures must be prevented (robust). This problem has been studied from different perspectives by different communities. However, the existing theory deals only with the case of quadratic costs (the LQ problem), which limits applications to stabilisation and tracking tasks only. In order to handle more general (non-convex) costs that naturally arise in many practical problems, we carefully select and bring together several tools from different communities, namely non-asymptotic linear regression, recent results in interval prediction, and tree-based planning. Combining and adapting the theoretical guarantees at each layer is non trivial, and we provide the first end-to-end suboptimality analysis for this setting. Interestingly, our analysis naturally adapts to handle many models and combines with a data-driven robust model selection strategy, which enables to relax the modelling assumptions. Last, we strive to preserve tractability at any stage of the method, that we illustrate on two challenging simulated environments.

cs.LG