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Related papers: A coordinate-free theory of virtual holonomic cons…

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The paper analyzes a Lagrangian system which is controlled by directly assigning some of the coordinates as functions of time, by means of frictionless constraints. In a natural system of coordinates, the equations of motions contain terms…

Optimization and Control · Mathematics 2015-05-13 A. Bressan , F. Rampazzo

For homogeneous bilinear control systems, the control sets are characterized using a Lie algebra rank condition for the induced systems on projective space. This is based on a classical Diophantine approximation result. For affine control…

Optimization and Control · Mathematics 2022-08-01 Fritz Colonius , Juliana Raupp , Alexandre J. Santana

Using techniques from the theory of von Neumann algebras, we propose a framework for addressing questions of controllability of bilinear systems on infinite dimensional Hilbert spaces. In the setup, we assume only that the drift and control…

Optimization and Control · Mathematics 2026-05-14 Dimitrios Giannakis , Gage Hoefer

We investigate necessary and sufficient conditions under which a general nonlinear affine control system with outputs can be written as a gradient control system corresponding to some pseudo-Riemannian metric defined on the state space. The…

Optimization and Control · Mathematics 2007-05-23 Jorge Cortes , Arjan van der Schaft , Peter E. Crouch

We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general…

Optimization and Control · Mathematics 2016-10-11 Andreas B. Hempel , Paul Goulart , John Lygeros

We consider a mechanical system which is controlled by means of moving constraints. Namely, we assume that some of the coordinates can be directly assigned as functions of time by means of frictionless constraints. This leads to a system of…

Classical Analysis and ODEs · Mathematics 2017-02-17 Alberto Bressan , Zipeng Wang

Model-based controllers can offer strong guarantees on stability and convergence by relying on physically accurate dynamic models. However, these are rarely available for high-dimensional mechanical systems such as deformable objects or…

Robotics · Computer Science 2026-02-10 Katharina Friedl , Noémie Jaquier , Seungyeon Kim , Jens Lundell , Danica Kragic

Systems subjected to holonomic constraints follow quite complicated dynamics that could not be described easily with Hamiltonian or Lagrangian dynamics. The influence of holonomic constraints in equations of motions is taken into account by…

Statistical Mechanics · Physics 2010-09-08 Martial Mazars

Underactuation is ubiquitous in human locomotion and should be ubiquitous in bipedal robotic locomotion as well. This chapter presents a coherent theory for the design of feedback controllers that achieve stable walking gaits in…

Robotics · Computer Science 2017-06-06 Jessy W Grizzle , Christine Chevallereau

Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…

Optimization and Control · Mathematics 2007-05-23 Anthony M. Bloch , Melvin Leok , Jerrold E. Marsden , Dmitry V. Zenkov

This article deals with the realisation of constraints in underdamped Langevin dynamics via soft-constrained dynamics. Specifically, we study systems with a large (or small) parameter that controls the constraint mechanisms, e.g. the…

Probability · Mathematics 2026-04-03 Carsten Hartmann , Lara Neureither , Upanshu Sharma

In this study, it is generalized the concept of Lagrangian mechanics with constraints to complex case. To be beginning, it is considered a Kaehlerian manifold as a velocity-phase space. Then a non-holonomic constraint is given by 1-form on…

Differential Geometry · Mathematics 2009-02-25 Mehmet Tekkoyun , Ali Gorgulu

Contact geometry allows to describe some thermodynamic and dissipative systems. In this paper we introduce a new geometric structure in order to describe time-dependent contact systems: cocontact manifolds. Within this setting we develop…

Mathematical Physics · Physics 2023-01-27 Manuel de León , Jordi Gaset , Xavier Gràcia , Miguel Carlos Muñoz-Lecanda , Xavier Rivas

Nonlinear systems of affine control inputs overarch many sensor fusion instances. Analyzing whether a state variable in such a nonlinear system can be estimated (i.e., observability) informs better estimator design. Among the research on…

Systems and Control · Electrical Eng. & Systems 2022-07-19 Jianzhu Huai , Yukai Lin , Yujia Zhang

The Helmholtz conditions are necessary and sufficient conditions for a system of second order differential equations to be variational, that is, equivalent to a system of Euler-Lagrange equations for a regular Lagrangian. On the other hand,…

Optimization and Control · Mathematics 2018-10-17 Marta Farré Puiggalí , Anthony M. Bloch

Lagrangian mechanics uses d'Alembert's principle of zero virtual work as an important starting point. The orthogonality of the force of constraint and virtual displacement is emphasized in literature, without a clear warning that this is…

Classical Physics · Physics 2007-05-23 Subhankar Ray , J. Shamanna

This article investigates the problem of enforcing a virtual holonomic constraint (VHC) on a mechanical system with degree of underactuation one while simultaneously stabilizing a closed orbit on the constraint manifold. This problem, which…

Dynamical Systems · Mathematics 2023-06-01 Alireza Mohammadi , Manfredi Maggiore , Luca Consolini

This paper presents a formulation of Lagrangian dynamics of constrained mechanical systems in terms of reduced quasi-velocities and quasi-forces that can be used for simulation, analysis, and control purposes. In this formulation, Cholesky…

Computational Physics · Physics 2021-08-17 Farhad Aghili

We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…

Optimization and Control · Mathematics 2023-02-09 Alberto De Marchi , Xiaoxi Jia , Christian Kanzow , Patrick Mehlitz

In this paper we study vakonomic dynamics on contact systems with nonlinear constraints. In order to obtain the dynamics, we consider a space of admisible paths, which are the ones tangent to a given submanifold. Then, we find the critical…

Mathematical Physics · Physics 2021-06-07 Manuel de León , Manuel Lainz , Miguel C. Muñoz-Lecanda