Related papers: Controllability and necessary second-order optimal…
This paper provides necessary conditions of optimality for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions cover fixed end-time problems and, under additional…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…
The necessary conditions for an optimal control of a stochastic control problem with recursive utilities is investigated. The first order condition is the the well-known Pontryagin type maximum principle. When the optimal control satisfying…
In this paper, we propose second-order sufficient optimality conditions for a very general nonconvex constrained optimization problem, which covers many prominent mathematical programs.Unlike the existing results in the literature, our…
This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of…
This paper aims to establish second order necessary conditions for optimal control in quantum stochastic systems. We employ a variational approach, analogous to methods in classical stochastic control, to analyze systems governed by quantum…
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…
In this research paper, we examine an optimal control problem involving a dynamical system governed by a nonlinear Caputo fractional time-delay state equation. The primary objective of this study is to obtain the necessary conditions for…
This short note shows how to solve optimal control problems using second order sensitivity analysis
An optimal control problem for a semilinear elliptic equation of divergence form is considered. Both the leading term and the semilinear term of the state equation contain the control. The well-known Pontryagin type maximum principle for…
A notion of $L^p$-exact controllability is introduced for linear controlled (forward) stochastic differential equations, for which several sufficient conditions are established. Further, it is proved that the $L^p$-exact controllability,…
In this article we study optimal control problems for systems that are affine in one part of the control variable. Finitely many equality and inequality constraints on the initial and final values of the state are considered. We investigate…
We give answer to an open question by proving a sufficient optimality condition for state-linear optimal control problems with time delays in state and control variables. In the proof of our main result, we transform a delayed state-linear…
It has recently been shown that the minimum energy solution of the control problem for a linear system produces a control trajectory that is nonlocal. An issue then arises when the dynamics represents a linearization of the underlying…
We study the singular stochastic optimal control problem with model uncertainty, where the necessary conditions determined by the corresponding maximum principle are trivial. Robust integral form and pointwise second order necessary…
The concept of a local infimum for an optimal control problem is introduced. This definition extends that of an optimal process. For a~local infimum we prove an existence theorem and derive necessary conditions that resemble some family of…
We consider optimal control problems governed by systems describing the unsteady flows of an incompressible second grade fluid with Navier-slip boundary conditions. We prove the existence of an optimal solution and derive the corresponding…
This paper studies a kind of minimal time control problems related to the exact synchronization for a controlled linear system of parabolic equations. Each problem depends on two parameters: the bound of controls and the initial state. The…
This paper is devoted to the controllability of linear systems of two coupled parabolic equations when the coupling involves a space dependent first order term. This system is set on an bounded interval, and the first equation is controlled…
In this article we study an optimal control problem subject to the Fokker-Planck equation \[ \partial_t \rho - \nu \Delta \rho - {\rm div } \big(\rho B[u]\big) = 0. \] The control variable $u$ is time-dependent and possibly…