Abstract Mathematical models of linear discrete-time set-valued Pareto-Nash-Stackelberg control processes are examined as extension of mono-valued Pareto-Nash-Stackelberg control models proposed by V. Ungureanu in [10]. A straightforward principle is applied to solve Pareto-Nash-Stackelberg control problems. Models and results are presented in natural order by beginning with the simplest case a...

Abstract. We study a class of mean-field stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H ∈ (1/2, 1) and a related stochastic control problem. We derive a Pontryagin type maximum principle and the associated adjoint mean-field backward stochastic differential equation driven by a classical Brownian motion, and we prove that under certain assumption...

Abstract. A problem of the model-based optimization of fed-batch cultivation process is solved for two control actions: feed-rate and dilution rate. A goal of optimization is to maximize the yield of cells’ biomass at the end of cultivation cycle. Two alternative optimization methods, based on the maximum principle of Pontryagin and the finite dimensional optimization approach, are developed fo...

The calculus of variations is an important tool in the study of boundary value problems for differential systems. A development of this approach, called the control variational method, is based on the use of the optimal control theory, especially of the Pontryagin maximum principle. In this presentation, we review the results established in the literature on the control variational method and i...

We consider in this paper, mixed relaxed-singular stochastic control problems, where the control variable has two components, the first being measure-valued and the second singular. The control domain is not necessarily convex and the system is governed by a nonlinear stochastic differential equation, in which the measure-valued part of the control enters both the drift and the diffusion coeffi...

Abstract: Problem statement: We studied the inventory-production system with two-parameter Weibull distributed deterioration items. Approach: The inventory model was developed as linear optimal control problem and by the Pontryagin maximum principle, the optimal control problem was solved analytically to obtain the optimal solution of the problem. Results: It was then illustrated with the help ...

This paper suggests some further developments in the theory of first-order necessary optimality conditions for problems of optimal control with infinite time horizons. We describe an approximation technique involving auxiliary finite-horizon optimal control problems and use it to prove new versions of the Pontryagin maximum principle. Special attention is paid to the behavior of the adjoint var...

In this paper we discuss the applications of the Hamilton-Pontryagin variational principle for designing time-adaptive variational integrators. First, we review the multisymplectic formalism of field theories. Next, we review the Hamilton-Pontryagin principle and show how it can be used to handle time reparametrizations in a very natural way. Finally, we derive a time-adaptive variational integ...

We study optimal control problems for hyperbolic equations (focusing on the multidimensional wave equation) with control functions in the Dirichlet boundary conditions under hard/pointwise control and state constraints. Imposing appropriate convexity assumptions on the cost integral functional, we establish the existence of optimal control and derive new necessary optimality conditions in the i...

This article treats two problems dealing with control of linear systems in the presence of a jammer that can sporadically turn off the control signal. The first problem treats the standard reachability problem, and the second treats the standard linear quadratic regulator problem under the above class of jamming signals. We provide necessary and sufficient conditions for optimality based on a n...