This note is concerned with an optimal control problem governed by the relativistic Maxwell-Newton-Lorentz equations, which describes the motion of charges particles in electro-magnetic fields and consists of a hyperbolic PDE system coupled with a nonlinear ODE. An external magnetic field acts as control variable. Additional control constraints are incorporated by introducing a scalar magnetic ...

This paper deals with optimal control problems of semilinear parabolic equations with pointwise state constraints and coupled integral state-control constraints. We obtain necessary optimality conditions in the form of a Pontryagin’s minimum principle for local solutions in the sense of Lp, p ≤ +∞.

The paper presents a numerical procedure for solving a class of optimal control problems for heterogeneous systems. The latter are described by parameterized systems of ordinary differential equations, coupled by integrals along the parameter space. Such problems arise in economics, demography, epidemiology, management of biological resources, etc. The numerical procedure include discretization...

Given an a ne system on a full-dimensional polytope, the problem of reaching a particular facet of the polytope, using continuous piecewise-a ne state feedback is studied. Necessary conditions and su cient conditions for the existence of a solution are derived in terms of linear inequalities on the input vectors at the vertices of the polytope. Special attention is paid to a ne systems on full-...

This paper concerns second order sufficient conditions of optimality, involving the Riccati equation, for optimal control problems with periodic boundary conditions. The problems considered involve no pathwise constraints and are ‘regular’, in the sense that the strengthened Legendre-Clebsch condition is assumed to be satisfied. A well-known sufficient condition, which we refer to as the Riccat...

A new algorithm is presented to solve both the finitehorizon time-varying and infinite-horizon timeinvariant discrete-time optimal reduced-order linear quadratic Gaussian (LQG) problem. In both cases the first order necessary optimality conditions can be represented by two non-linearly coupled discrete-time Lyapunov equations, which run forward and backward in discrete time. The algorithm itera...

In this article, we study the large time behavior of solutions of first-order Hamilton-Jacobi Equations, set in a bounded domain with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish general convergence results for viscosity solutions of these Cauchy-Neumann problems by using two fairly different methods : the first one relies only on part...

In this paper, we consider stochastic optimal control of Markov Jump Linear Systems with state feedback but without observation of the jumping parameter. The proposed control law is assumed to be linear with constant gains that can be obtained from the necessary optimality conditions using an iterative algorithm. The proposed approach is demonstrated in a numerical example.

Optimal control under state constraints has brought new mathematical challenges that have led to new techniques and new theories. We survey some recent results related to issues of regularity of optimal trajectories, optimal controls and the value function, and discuss optimal synthesis and necessary optimality conditions. We also show how abstract inverse mapping theorems of set-valued analysi...

We consider a stochastic control problem, where the control domain is convex and the system is governed by a nonlinear backward stochastic differential equation. With a L1 terminal data, we derive necessary optimality conditions in the form of stochastic maximum principle. AMS Subject Classification. 93Exx