Related papers: First and Second Order Necessary Optimality Condit…
In this paper we prove a necessary condition of the optimal control problem for a class of general mean-field forward-backward stochastic systems with jumps in the case where the diffusion coefficients depend on control, the control set…
In this work, we address some optimal control problems related to the evolution of two isothermal, incompressible, immisible fluids in a two dimensional bounded domain. A distributed optimal control problem is formulated as the minimization…
The work is organized as follows. First an introduction is given in Chapter 1. In Chapter 2 we introduce the POD method in finite and infinite-dimensional Hilbert spaces and discuss various applications. Chapter 3 is devoted to to POD-based…
Optimal control problems of forward stochastic Volterra integral equations (SVIEs) are formulated and studied. When control region is arbitrary subset of Euclidean space and control enters into the diffusion, necessary conditions of…
This paper investigates the optimal control of a bilinear damped wave equation over an infinite time horizon. We establish the well-posedness of the controlled system and derive uniform energy estimates. The existence of optimal controls is…
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…
In this paper we derive new second-order optimality conditions for a very general set-constrained optimization problem where the underlying set may be nononvex. We consider local optimality in specific directions (i.e., optimal in a…
This paper develops a comprehensive extension of the $\Lambda$-set framework for optimal control, introducing second-order $\Lambda$-sets and generalizing the theory to non-smooth, hybrid, and stochastic hybrid systems. We first establish…
A method of optimal control computation is proposed for problems with control and state constraints. It uses a sequence of control structure adjustments in the form of generations and reductions of nodes and arcs, which do not change the…
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…
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…
This paper is concerned with impulse approximate controllability for stochastic evolution equations with impulse controls. As direct applications, we formulate captivating minimal norm and time optimal control problems; The minimal norm…
In this paper, we consider an optimal control problem for the two-dimensional evolutionary Navier-Stokes system. Looking for sparsity, we take controls as functions of time taking values in a space of Borel measures. The cost functional…
This paper is concerned with first- and second-order optimality conditions as well as the stability for non-smooth semilinear optimal control problems involving the $L^1$-norm of the control in the cost functional. In addition to the…
In this paper we study the optimal control of a parabolic initial-boundary value problem of Allen--Cahn type with dynamic boundary conditions. Phase field systems of this type govern the evolution of coupled diffuse phase transition…
Stochastic optimal control problems with constraints on the probability distribution of the final output are considered. Necessary conditions for optimality in the form of a coupled system of partial differential equations involving a…
The paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and constrained optimization problems in finite-dimensional spaces.…
The aim of this work is to study the optimal control problems of flows governed by the incompressible third grade fluid equations with Navier-slip boundary conditions. After recalling a result on the well-posedness of the state equations,…
We consider constrained bilinear optimal control of second-order linear evolution partial differential equations (PDEs) with a reaction term on the half line, where control arises as a time-dependent reaction coefficient and constraints are…
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…