activity
20172026
most citedOn a class of generating vector fields for the extremum seeking problem: Lie bracket approximation and stability properties

108 citations · 179 across the 18 of their papers we have counts for

collaborators

19 papers

cs.CL2026

LoWAgent: A Low-Resource Multilingual Benchmark for Web Agents

Ocean Monjur, Daud Ahmad Nisar, Shahriar Kabir Nahin +4

Web agents are typically evaluated on English-language interfaces, leaving their ability to operate across the world's multilingual websites largely unexplored. This gap is especia…

math.OC2026

Lie bracket approximations of RMSprop for Extremum Seeking Control

Victoria Grushkovskaya, Christian Ebenbauer

This paper presents novel extremum seeking algorithms inspired by RMSProp dynamics and based on Lie bracket approximation techniques. To inherit the behavior of the classical conti…

math.OC2026

Extremum seeking with exponential convergence via high-order Lie bracket approximations

Victoria Grushkovskaya, Sameh A. Eisa

This paper focuses on the further development of the Lie bracket approximation approach for optimization and control via extremum seeking systems. Classical results in this area pr…

math.OC2026

Implementation of Time-Varying Controllers for a Nonholonomic Mobile Robot: Experimental Studies

Alexander Zuyev, Victoria Grushkovskaya, Sebastian Eisner

We consider a kinematic model of a wheeled mobile robot controlled by translational and angular velocities. For this class of nonholonomic systems, a family of time-varying feedbac…

math.OC2025★ 1 cited

Model-free source seeking of exponentially convergent unicycle: theoretical and robotic experimental results

Rohan Palanikumar, Ahmed A. Elgohary, Victoria Grushkovskaya +1

This paper introduces a novel model-free, real-time unicycle-based source seeking design. This design autonomously steers the unicycle dynamic system towards the extremum point of…

math.OC2025

Extremum Seeking with High-Order Lie Bracket Approximations: Achieving Exponential Decay Rate

Victoria Grushkovskaya, Sameh A. Eisa

This paper focuses on the further development of the Lie bracket approximation approach for extremum seeking systems. Classical results in this area provide extremum seeking algori…

math.OC2025★ 1 cited

On classical solutions in the stabilization problem for nonholonomic control systems with time-varying feedback laws

Alexander Zuyev, Victoria Grushkovskaya

We consider the stabilization problem for driftless control-affine systems under the bracket-generating condition. In our previous works, a class of time-varying feedback laws has…

math.OC2024★ 2 cited

Stabilization of a Nonholonomic Car Model with Off-Hooked Trailers

Alexander Zuyev, Victoria Grushkovskaya

We consider a kinematic model of a controlled car with two trailers by assuming that each trailer is attached at some distance from the preceding axle ("off-hooked trailers"). For…

math.OC2023

Partial stabilization of nonlinear systems along a given trajectory

Victoria Grushkovskaya, Iryna Vasylieva, Alexander Zuyev

In this paper, the problem of partial stabilization of nonlinear systems along a given trajectory is considered. This problem is treated within the framework of stability of a fami…

math.OC2023★ 10 cited

Motion planning and stabilization of nonholonomic systems using gradient flow approximations

Victoria Grushkovskaya, Alexander Zuyev

Nonlinear control-affine systems with time-varying vector fields are considered in the paper. We propose a unified control design scheme with oscillating inputs for solving the tra…

math.OC2020★ 4 cited

Extremum Seeking Approach for Nonholonomic Systems with Multiple Time Scale Dynamics

Victoria Grushkovskaya, Alexander Zuyev

In this paper, a class of nonlinear driftless control-affine systems satisfying the bracket generating condition is considered. A gradient-free optimization algorithm is developed…

math.OC2020★ 2 cited

Partial stabilization of nonholonomic systems with application to multi-agent coordination

Victoria Grushkovskaya, Alexander Zuyev

This paper focuses on the problem of constructing time-varying feedback laws that asymptotically stabilize a given part of the state variables for nonlinear control-affine systems.…

math.OC2019★ 1 cited

On exponential stabilization of nonholonomic systems with time-varying drift

Victoria Grushkovskaya, Alexander Zuyev

A class of nonlinear control-affine systems with bounded time-varying drift is considered. It is assumed that the control vector fields together with their iterated Lie brackets sa…

math.OC2019★ 9 cited

Partial Stability Concept in Extremum Seeking Problems

Victoria Grushkovskaya, Alexander Zuyev

The paper deals with the extremum seeking problem for a class of cost functions depending only on a part of state variables of a control system. This problem is related to the conc…

math.OC2019★ 5 cited

Stabilization of non-admissible curves for a class of nonholonomic systems

Victoria Grushkovskaya, Alexander Zuyev

The problem of tracking an arbitrary curve in the state space is considered for underactuated driftless control-affine systems. This problem is formulated as the stabilization of a…

math.OC2019★ 5 cited

On stabilization of nonlinear systems with drift by time-varying feedback laws

Alexander Zuyev, Victoria Grushkovskaya

This paper deals with the stabilization problem for nonlinear control-affine systems with the use of oscillating feedback controls. We assume that the local controllability around…

math.OC2018★ 17 cited

Obstacle Avoidance Problem for Second Degree Nonholonomic Systems

Victoria Grushkovskaya, Alexander Zuyev

In this paper, we propose a new control design scheme for solving the obstacle avoidance problem for nonlinear driftless control-affine systems. The class of systems under consider…

math.OC2018★ 14 cited

A family of extremum seeking laws for a unicycle model with a moving target: theoretical and experimental studies

Victoria Grushkovskaya, Simon Michalowsky, Alexander Zuyev +2

In this paper, we propose and practically evaluate a class of gradient-free control functions ensuring the motion of a unicycle-type system towards the extremum point of a time-var…

math.OC2017★ 108 cited

On a class of generating vector fields for the extremum seeking problem: Lie bracket approximation and stability properties

Victoria Grushkovskaya, Alexander Zuyev, Christian Ebenbauer

In this paper, we describe a broad class of control functions for extremum seeking problems. We show that it unifies and generalizes existing extremum seeking strategies which are…