相关论文: Gauge Symmetries and Noether Currents in Optimal C…

We give a new computational method to obtain symmetries of ordinary differential equations. The proposed approach appears as an extension of a recent algorithm to compute variational symmetries of optimal control problems [Comput. Methods…

This note is concerned with an optimal control problem governed by the relativistic Maxwell-Newton-Lorentz equations, which describes the motion of charges particles in electro-magnetic fields and consists of a hyperbolic PDE system coupled…

We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary…

Along the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. {\bf 110} (2003), 723; {\it ibid}, {\bf 113} (2005), 481.], we formulate the second order gauge invariant…

We study the reduction of degrees of freedom for the equations that determine necessary optimality conditions for extrema in an optimal control problem for a multiagent system by exploiting the physical symmetries of agents, where the…

Noether's theorem in the realm of point dynamics establishes the correlation of a constant of motion of a Hamilton-Lagrange system with a particular symmetry transformation that preserves the form of the action functional. Although usually…

A geometric framework, called multicontact geometry, has recently been developed to study action-dependent field theories. In this work, we use this framework to analyze symmetries in action-dependent Lagrangian and Hamiltonian field…

We obtain a nonsmooth extension of Noether's symmetry theorem for variational problems with delayed arguments. The result is proved to be valid in the class of Lipschitz functions, as long as the delayed Euler-Lagrange extremals are…

General Lagrangian theory of even and odd fields on an arbitrary smooth manifold is considered. Its non-trivial reducible gauge symmetries and their algebra are defined in this very general setting by means of the inverse second Noether…

A class of optimal control problems of hybrid nature governed by semilinear parabolic equations is considered. These problems involve the optimization of switching times at which the dynamics, the integral cost, and the bounds on the…

We study local controllability and optimal control problems for invertible discrete-time control systems. We present second order necessary conditions for optimality and sufficient conditions for local controllability. The conditions are…

The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…

We consider an optimal control problem governed by an elliptic variational inequality of the second kind. The problem is discretized by linear finite elements for the state and a variational discrete approach for the control. Based on a…

This work is concerned with second-order necessary and sufficient optimality conditions for optimal control of a non-smooth semilinear elliptic partial differential equation, where the nonlinearity is the non-smooth max-function and thus…

This paper is devoted to the study of mechanical systems subjected to external forces in the framework of symplectic geometry. We obtain a Noether's theorem for Lagrangian systems with external forces, among other results regarding…

In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an…

We apply Noether's theorem to show how the invariances of conservative systems are broken for nonconservative systems, in the variational formulation of Galley. This formulation considers a conservative action, extended by the inclusion of…

In this paper we study optimal control problems for nonholonomic systems defined on Lie algebroids by using quasi-velocities. We consider both kinematic, i.e. systems whose cost functional depends only on position and velocities, and…

In this paper, we formulate a distributed optimal control problem related to the evolution of two isothermal, incompressible, immiscible fluids in a two dimensional bounded domain. The distributed optimal control problem is framed as the…

The purpose of this paper is to review and highlight some connections between the problem of nonlinear smoothing and optimal control of the Liouville equation. The latter has been an active area of recent research interest owing to work in…