Related papers: Second order necessary and sufficient optimality c…
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 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 establish new second order necessary and sufficient optimality conditions for a class of control-affine problems with a scalar control and a scalar state constraint. These optimality conditions extend to the constrained…
In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with…
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…
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…
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…
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 paper puts forward sufficient conditions for local controllability of a control dynamical system. The results obtained are meaningful in the case when the linear approximation to this system is not completely controllable. As a…
In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with…
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…
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…
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…
Higher order necessary conditions for a minimizer of an optimal control problem are generally obtained for systems whose dynamics is continuously differentiable in the state variable. Here, by making use of the notion of set-valued Lie…
We study nonlinear singular optimal control problems of port-Hamil-tonian (descriptor) systems. We employ general control-affine cost functionals that include as a special case the energy supplied to the system. We first derive optimality…
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…
In this paper, we are concerned with optimal control problems evolved on Riemannian manifolds, where the initial and final states satisfy some inequality and equality type constraints, and the control set is a separable metric space. We…
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…
In this article we propose a shooting algorithm for optimal control problems governed by systems that are affine in one part of the control variable. Finitely many equality constraints on the initial and final state are considered. We…
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…