相关论文: Noether's Theorem for Fractional Optimal Control P…

We consider an optimal control problem governed by a class of boundary value problem with the spectral Dirichlet fractional Laplacian. Some sufficient condition for the existence of optimal processes is stated. The proof of the main result…

In this article, we study a fractional control problem that models the maximization of the profits obtained by exploiting a certain resource whose dynamics are governed by the fractional logistic equation. Due to the singularity of this…

We propose and study an optimal control model for malaria infection described by system of fractional differential equations. The model is formulated in terms of the left and right Caputo fractional derivatives. We determine the necessary…

In this paper, we consider the approximate controllability of partial differential equations with time derivatives of non-integer order via boundary control. We first show the unique existence of the solution under smooth boundary…

A general study of symmetries in optimal control theory is given, starting from the presymplectic description of this kind of system. Then, Noether's theorem, as well as the corresponding reduction procedure (based on the application of the…

The aim of this notes is to give a concise introduction to control theory for systems governed by stochastic partial differential equations. We shall mainly focus on controllability and optimal control problems for these systems. For the…

In this paper, the fractional order Hegselmann-Krause type model with leadership is studied.We seek an optimal control strategy for the system to reach a consensus in such a way that the control mechanism is included in the leader dynamics.…

We study variational systems for space curves, for which the Lagrangian or action principle has a Euclidean symmetry, using the Rotation Minimising frame, also known as the Normal, Parallel or Bishop frame. Such systems have previously been…

We prove necessary optimality conditions of Pontryagin type for a class of fuzzy fractional optimal control problems with the fuzzy fractional derivative described in the Caputo sense. The new results are illustrated by computing the…

Noether theorem establishes an interesting connection between symmetries of the action integral and conservation laws of a dynamical system. The aim of the present work is to classify the damped harmonic oscillator problem with respect to…

The present work addresses a finite-horizon linear-quadratic optimal control problem for uncertain systems driven by piecewise constant controls. The precise values of the system parameters are unknown, but assumed to belong to a finite set…

Different fractional difference types of Euler-Lagrange equations are obtained within Riemann and Caputo by making use of different versions of integration by part forumlas in fractional difference calculus. An example is presented to…

This work considers the problem of approximating initial condition and time-dependent optimal control and trajectory surfaces using multivariable Fourier series. A modified Augmented Lagrangian algorithm for translating the optimal control…

We establish a new version of the first Noether Theorem, according to which the (equivalence classes of) first integrals of given Euler-Lagrange equations in one independent variable are in exact one-to-one correspondence with the…

Through duality it is possible to transform left fractional operators into right fractional operators and vice versa. In contrast to existing literature, we establish integration by parts formulas that exclusively involve either left or…

The first and second Noether theorems are formulated in a general case of reducible degenerate Grassmann-graded Lagrangian theory of even and odd variables on graded bundles. Such Lagrangian theory is characterized by a hierarchy of…

Noether's Theorem is familiar to most physicists due its fundamental role in linking the existence of conservation laws to the underlying symmetries of a physical system. Typically the systems are described in the particle-based context of…

This paper provides a modern presentation of Noether's theory in the realm of classical dynamics, with application to the problem of a particle submitted to both a potential and a linear dissipation. After a review of the close…

One of the motivations for using fractional calculus in physical systems is due to fact that many times, in the space and time variables we are dealing which exhibit coarse-grained phenomena, meaning that infinitesimal quantities cannot be…

The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…