Related papers: Controllability and necessary second-order optimal…
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…
It has been shown recently that optimal control problems with the dynamical constraint given by a second order system admit a regular Lagrangian formulation. This implies that the optimality conditions can be obtained in a new form based on…
Second-order necessary conditions for optimal control problems are considered, where the ``second-order" is in the sense of that Pontryagin's maximum principle is viewed as a first-order necessary optimality condition. A sufficient…
For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…
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 study a control problem governed by a semilinear parabolic equation with pointwise control and state constraints imposed at every point of the space-time cylinder. We obtain second order sufficient optimality conditions for local…
This paper is concerned with second-order optimality conditions for Tikhonov regularized optimal control problems governed by the obstacle problem. Using a simple observation that allows to characterize the structure of optimal controls on…
This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with…
A class of time-optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints and final point constraints is considered. By introducing the so-called locally optimal solution to time-optimal control…
The main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach. The control system is governed by a stochastic…
This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain…
In this article we study optimal control problems for systems that are affine with respect to some of the control variables and nonlinear in relation to the others. We consider finitely many equality and inequality constraints on the…
This paper proposes an optimal control problem for a parabolic equation with a nonlocal nonlinearity. The system is described by a parabolic equation involving a nonlinear term that depends on the solution and its integral over the domain.…
In this work, we consider the two dimensional tidal dynamics equations in a bounded domain and address some optimal control problems like total energy minimization, minimization of dissipation of energy of the flow, etc. We also examine an…
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…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we…
This paper is the second part of our series of work to establish pointwise second-order necessary conditions for stochastic optimal controls. In this part, we consider the general cases, i.e., the control region is allowed to be nonconvex,…
The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms. When the control…
The purpose of this paper is to establish the first and second order necessary conditions for stochastic optimal controls in infinite dimensions. The control system is governed by a stochastic evolution equation, in which both drift and…
The main purpose of this paper is the study of second-order optimality conditions for the bilinear control of a strongly degenerate parabolic equation. The equation is degenerate at the boundary of the spatial domain. The well-posedness of…