Related papers: Noether theorem in stochastic optimal control prob…
Optimal control problems are usually addressed with the help of the famous Pontryagin Maximum Principle (PMP) which gives a generalization of the classical Euler-Lagrange and Weierstrass necessary optimality conditions of the calculus of…
We consider the control problem of the stochastic Navier-Stokes equations in multidimensional domains introduced in \cite{ocpc} restricted to noise terms defined by Q-Wiener processes. Using a stochastic maximum principle, we derive a…
In this paper, we explore a new class of stochastic control problems characterized by specific control constraints. Specifically, the admissible controls are subject to the ratcheting constraint, meaning they must be non-decreasing over…
This paper is concerned with the existence of optimal controls for backward stochastic partial differential equations with random coefficients, in which the control systems are represented in an abstract evolution form, i.e. backward…
It's well known that Noether symmetries lead to the conservation laws. Conserved quantities are constructed out of generator of the symmetry - invariant Hamiltonian vector field. Considering more general class of vector fields -…
In this note, we propose a symplectic algorithm for the stable manifolds of the Hamilton-Jacobi equations combined with an iterative procedure in [Sakamoto-van~der Schaft, IEEE Transactions on Automatic Control, 2008]. Our algorithm…
In this paper we study a class of stochastic control problems in which the control of the jump size is essential. Such a model is a generalized version for various applied problems ranging from optimal reinsurance selections for general…
An infinite sequence of commuting nonpolynomial contact symmetries of the two-dimensional minimal surface equation is constructed. Local and nonlocal conservation laws for $n$-dimensional minimal area surface equation are obtained by using…
A canonical Hamiltonian is found for a reduced version of the Jackiw-Pi model for bilayer graphene. From the corresponding Lagrangian, the Noether point symmetries and conserved quantities are determined. The Noether symmetry group is the…
Many applications require solving non-linear control problems that are classically not well behaved. This paper develops a simple and efficient chattering algorithm that learns near optimal decision policies through an open-loop feedback…
The aim of the paper is to study an optimal control problem on infinite horizon for an infinite dimensional integro-differential equation with completely monotone kernelskernels, where we assume that the noise enters the system when we…
We consider the optimal control of quantum systems interacting non-linearly with an electromagnetic field. We propose new monotonically convergent algorithms to solve the optimal equations. The monotonic behavior of the algorithm is ensured…
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 obtain a discrete time analog of E. Noether's theorem in Optimal Control, asserting that integrals of motion associated to the discrete time Pontryagin Maximum Principle can be computed from the quasi-invariance properties of the…
We study an inverse problem of the stochastic optimal control of general diffusions with performance index having the quadratic penalty term of the control process. Under mild conditions on the system dynamics, the cost functions, and the…
The aim of this paper is to investigate the existence of optimal controls for systems described by stochastic partial differential equations (SPDEs) with locally monotone coefficients controlled by different external forces which are…
We develop a general theoretical framework for optimal probability density control on standard measure spaces, aimed at addressing large-scale multi-agent control problems. In particular, we establish a maximum principle (MP) for control…
In this paper, we investigate a fully nonlinear evolutionary Hamilton-Jacobi-Bellman (HJB) parabolic equation utilizing the monotone operator technique. We consider the HJB equation arising from portfolio optimization selection, where the…
We consider a Bayesian adaptive optimal stochastic control problem where a hidden static signal has a non-separable influence on the drift of a noisy observation. Being allowed to control the specific form of this dependence, we aim at…
We prove a Noether-type symmetry theorem for invariant optimal control problems with unrestricted controls. The result establishes weak conservation laws along all the minimizers of the problems, including those minimizers which do not…