相关论文: Inexact trajectory planning and inverse problems i…

Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…

This paper studies the reduction by symmetry of variational problems on Lie groups and Riemannian homogeneous spaces. We derive the reduced equations of motion in the case of Lie groups endowed with a left-invariant metric, and on Lie…

Several aspects of the connection between conserved integrals (invariants) and symmetries are illustrated within a hybrid Lagrangian-Hamiltonian framework for dynamical systems. Three examples are considered: a nonlinear oscillator with…

In this paper we present a general framework that allows one to study discretization of certain dynamical systems. This generalizes earlier work on discretization of Lagrangian and Hamiltonian systems on tangent bundles and cotangent…

In this contribution we present an intrinsic description of time-variant Port Hamiltonian systems as they appear in modeling and control theory. This formulation is based on the splitting of the state bundle and the use of appropriate…

Through the Pontryagin maximum principle, we solve a minimal-time problem for a linear control system on a cylinder, considered as a homogeneous space of the solvable Lie group of dimension two. The main result explicitly shows the…

We consider the problem of optimal path planning in different homotopy classes in a given environment. Though important in robotics applications, path-planning with reasoning about homotopy classes of trajectories has typically focused on…

In this paper we study reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent control systems, with partial symmetry breaking cost functions. Our approach emphasizes the role of…

The study of problems of the calculus of variations with compositions is a quite recent subject with origin in dynamical systems governed by chaotic maps. Available results are reduced to a generalized Euler-Lagrange equation that contains…

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…

In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian…

A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of Hamiltonian vector…

The problem of real-time control and optimization of components' routing in discrete manufacturing plants, where distinct items must undergo a sequence of jobs, is considered. This problem features a large number of discrete control inputs…

Efficient path planning for autonomous mobile robots is a critical problem across numerous domains, where optimizing both time and energy consumption is paramount. This paper introduces a novel methodology that considers the dynamic…

By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system…

We study control systems invariant under a Lie group with application to the problem of nonlinear trajectory planning. A theory of symmetry reduction of exterior differential systems is employed to demonstrate how symmetry reduction and…

We formulate nonlinear nonlocal integro-PDE with memory, biloaded (boundary integrals load the ambient space, and the ambient space loads the boundary), and the associated optimal control problems. We derive part of the necessary conditions…

Invariant Lagrangians yield invariant Euler-Lagrange equations, and it was discussed in the literature how to compute those using various local methods. The focus of this paper is on global algebraic differential invariants. In this case…

Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization maps can be conveniently lifted to a…

In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are…