Related papers: Geometric control theory of vertical rolling disc …
Symmetries, e.g. rotational and translational invariances for the class of mechanical systems, allow to characterize solution trajectories of nonlinear dynamical systems. Thus, the restriction to symmetry-induced dynamics, e.g. by using the…
This work develops a symmetry-based framework for formation control on cycle graphs using Dihedral point-group constraints. We show that enforcing inter-agent reflection symmetries, together with anchoring a single designated agent to its…
We apply methods of the so-called `inverse problem of the calculus of variations' to the stabilization of an equilibrium of a class of two-dimensional controlled mechanical systems. The class is general enough to include, among others, the…
Ensemble control offers rich and diverse opportunities in mathematical systems theory. In this paper, we present a new paradigm of ensemble control, referred to as distributional control, for ensemble systems. We shift the focus from…
We consider a terminal control problem for processes governed by a nonlinear system of fractional ODEs. In order to show existence of the control, we first consider the linear counterpart of the system and reprove a number of classical…
Motivated by mechanical systems with symmetries, we focus on optimal control problems possessing symmetries. Following recent works, which generalized the classical concept of static turnpike to manifold turnpike, we extend the exponential…
This paper presents decentralized algorithms for formation control of multiple robots in three dimensions. Specifically, we leverage the mathematical properties of cyclic pursuit along with results from contraction and partial contraction…
We study a time minimization problem on the group of motions of a plane with admissible control in a half-disk. The considered control system describes a model of a car that can move forward on a plane and turn in place. Optimal…
In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to…
The purpose of this thesis is to study classical combinatorial objects, such as polytopes, polytopal complexes, and subspace arrangements, using tools that have been developed in combinatorial topology, especially those tools developed in…
In this review paper, we consider three kinds of systems of differential equations, which are relevant in physics, control theory and other applications in engineering and applied mathematics; namely: Hamilton equations, singular…
We discuss the problems of modeling, control, and decision support in complex dynamic systems from a general system theoretic point of view. The main characteristics of complex systems and of system approach to complex system study are…
This is a brief introduction to control theory in finite-dimensional spaces. The material is partly based on my lectures for the Master 1 program in Math\'ematiques et applications at Sorbonne University, delivered over the past few years.…
The selection of an appropriate control strategy is essential for ensuring safe operation in autonomous driving. While numerous control strategies have been developed for specific driving scenarios, a comprehensive comparative assessment of…
Control theory of dynamical systems offers a powerful framework for tackling challenges in deep neural networks and other machine learning architectures. We show that concepts such as simultaneous and ensemble controllability offer new…
We study dynamics of an wheeled inverted pendulum under a proportional-integral-derivative controller on horizontal, inclined and soft surfaces. An oscillatory area and conditions of the stability for the control are shown on the phase…
Dynamical System (DS)-based closed-loop control is a simple and effective way to generate reactive motion policies that well generalize to the robotic workspace, while retaining stability guarantees. Lately the formalism has been expanded…
Stochastic Optimal Control (SOC) problems arise in systems influenced by uncertainty, such as autonomous robots or financial models. Traditional methods like dynamic programming are often intractable for high-dimensional, nonlinear systems…
In this paper we study the mixed virtual element approximation to an elliptic optimal control problem with boundary observations. The objective functional of this type of optimal control problem contains the outward normal derivatives of…
The oblique basis method is reviewed from engineering point of view related to vibration and control theory. Examples are used to demonstrate and relate the oblique basis in nuclear physics to the equivalent mathematical problems in…