Related papers: Nonconservative Noether's Theorem in Optimal Contr…
This paper deals with an optimal control problem and describes the reachable set for the scalar 1-D conservation laws with discontinuous flux. Regarding the optimal control problem we first prove the existence of a minimizer and then we…
In Ref.~\cite{Sag} we proposed a geometric formulation of generalized Nambu mechanics. In the present paper we extend the class of Nambu systems by replacing the stringent condition of constancy of 3-form by closedness. We also explore the…
Physical systems are modeled by field equations; these are coupled, partial differential equations in space and time. Field equations are often given by balance equations and constitutive equations, where the former are axiomatically given…
Understanding complex systems with their reduced model is one of the central roles in scientific activities. Although physics has greatly been developed with the physical insights of physicists, it is sometimes challenging to build a…
Here we derive a nonsmooth maximum principle for optimal control problems with both state and mixed constraints. Crucial to our development is a convexity assumption on the "velocity set". The approach consists of applying known…
It has been asserted previously by the author that optimal control theory can be a valuable framework for theoretical studies about the shape that a wind instrument should have in order to satisfy some optimization criterion, inside a…
In this note, we consider an optimal control problem associated to a differential equation driven by a H\"{o}lder continuous function g of index greater than 1/2. We split our study in two cases. If the coefficient of dg\_t does not depend…
We obtain a nonsmooth higher-order extension of Noether's symmetry theorem for variational isoperimetric problems with delayed arguments. The result is proved to be valid in the class of Lipschitz functions, as long as the delayed…
We develop a non-anticipating calculus of variations for functionals on a space of laws of continuous semi-martingales, which extends the classical one. We extend Hamilton's least action principle and Noether's theorem to this generalized…
Noether's celebrated theorem associating symmetry and conservation laws in classical field theory is adapted to allow for broken symmetry in geometric mechanics and is shown to play a central role in deriving and understanding the…
In the present paper geometric aspects of relationship between non-Noether symmetries and conservation laws in Hamiltonian systems is discussed. It is shown that integrals of motion associated with continuous non-Noether symmetry are in…
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…
The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…
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…
We review the Lagrangian formulation of Noether symmetries (as well as "generalized Noether symmetries") in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called "Natural Theories" and "Gauge-Natural…
We derive conservation and balance laws for the translational gauge theory of dislocations by applying Noether's theorem. We present an improved translational gauge theory of dislocations including the dislocation density tensor and the…
An optimal control problem for the continuity equation is considered. The aim of a "controller" is to maximize the total mass within a target set at a given time moment. The existence of optimal controls is established. For a particular…
Two applications of the Noether method for fluids and plasmas are presented based on the Euler-Lagrange and Euler-Poincare variational principles, which depend on whether the dynamical fields are to be varied independently or not,…
In this manuscript, we consider a control system governed by a general ordinary differential equation on a Riemannian manifold, with its endpoints satisfying some inequalities and equalities, and its control constrained to a closed convex…
The paper is devoted to the study of a new class of optimal control problems for nonsmooth dynamical systems governed by nonconvex discontinuous differential inclusions of the sweeping type with involving variable time into optimization. We…