Modeling the dynamics of infectious diseases, illicit drug initiation, or other systems, where the age of an individual or the duration of being in a specific state is essential, leads to a generalized form of the McKendrick equations, i.e., a system of first-order partial differential equations in the time-age space. Typically such models include agespecific feedback components which are repre...

We analyze the structure of the linear differential and difference operators associated with the necessary optimality conditions of optimal control problems for descriptor systems in continuousand discrete-time. It has been shown in [27] that in continuous-time the associated optimality system is a self-conjugate operator associated with a self-adjoint pair of coefficient matrices and we show t...

In this paper, we study the asymptotic behaviour of a parabolic optimal control problem in a domain Ωε ⊂ Rn , whose boundary ∂Ωε contains a highly oscillating part. We consider this problem with two different classes of Dirichlet boundary controls, and, as a result, we provide its asymptotic analysis with respect to the different topologies of homogenization. It is shown that the mathematical d...

In this paper, we study second-order necessary optimality conditions for a discrete optimal control problem with nonconvex cost functions and state-control constraints. By establishing an abstract result on second-order necessary optimality conditions for a mathematical programming problem, we derive second-order necessary optimality conditions for a discrete optimal control problem.

We consider an optimal control problem governed by an ODE with memory playing the role of a control. We show the existence of an optimal solution and derive some necessary optimality conditions. Some examples are then discussed.

In this paper we study a class of Mayer-type hybrid optimal control problems. Using Lagrange techniques, we formulate a version of the Hybrid Maximum Principle for optimal control problems governed by hybrid systems with autonomous location transitions in the presence of additional target constraints.

Abstract. In this paper, we investigate the optimal control of the Burgers equation. For both optimal distributed and (Neumann) boundary control problems, the Dubovitskii and Milyutin functional analytical approach is adopted in investigation of the Pontryagin maximum principles of the systems. The necessary optimality conditions are, respectively, presented for two kinds of optimal control pro...

The paper presents necessary optimality conditions of Pontryagin’s type for infinite-horizon optimal control problems for age-structured systems with stateand control-dependent boundary conditions. Despite the numerous applications of such problems in population dynamics and economics, a “complete” set of optimality conditions is missing in the existing literature, because it is problematic to ...

For an optimal control problem with fixed initial state and constraints on admissible controls we propose new second-order necessary optimality conditions using second-order tangents to the set of controls. In the absence of constraints on controls, our conditions are stronger than those of Gilbert and Bernstein (1983). Then, we investigate optimal control problems with fixed initial state and ...

supersonic separators have found extensive applications in dehumidification of natural gases since 2003. unlike previous studies, which have investigated the inlet conditions and nozzle geometry of supersonic separators for pure fluids, the present study employed a combination of momentum, heat, and mass transfer equations along with virial equation of state (eos) to inspect the effect of inlet...