Optimal Control of a Stefan Problem with State-Space Constraints.
Optimal control of a variational inequality with possibly nonsymmetric linear operator. Application to the obstacle problems in mathematical physics.
Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity
Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity
We study here an optimal control problem for a semilinear elliptic equation with an exponential nonlinearity, such that we cannot expect to have a solution of the state equation for any given control. We then have to speak of pairs (control, state). After having defined a suitable functional class in which we look for solutions, we prove existence of an optimal pair for a large class of cost functions using a non standard compactness argument. Then, we derive a first order optimality system assuming...
Optimal control of an inventory system with ameliorating and deteriorating items.
Optimal control of combined therapy in a single strain HIV-1 model.
Optimal control of constrained delay-differential inclusions with multivalued initial conditions
Optimal control of delay systems with differential and algebraic dynamic constraints
This paper concerns constrained dynamic optimization problems governed by delay control systems whose dynamic constraints are described by both delay-differential inclusions and linear algebraic equations. This is a new class of optimal control systems that, on one hand, may be treated as a specific type of variational problems for neutral functional-differential inclusions while, on the other hand, is related to a special class of differential-algebraic systems with a general delay-differential...
Optimal control of delay systems with differential and algebraic dynamic constraints
This paper concerns constrained dynamic optimization problems governed by delay control systems whose dynamic constraints are described by both delay-differential inclusions and linear algebraic equations. This is a new class of optimal control systems that, on one hand, may be treated as a specific type of variational problems for neutral functional-differential inclusions while, on the other hand, is related to a special class of differential-algebraic systems with a general delay-differential...
Optimal control of fluid flow in soil 1. Deterministic case.
We study the numerical aspect of the optimal control of problems governed by a linear elliptic partial differential equation (PDE). We consider here the gas flow in porous media. The observed variable is the flow field we want to maximize in a given part of the domain or its boundary. The control variable is the pressure at one part of the boundary or the discharges of some wells located in the interior of the domain. The objective functional is a balance between the norm of the flux in the observation...
Optimal control of impulsive stochastic evolution inclusions
In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions driven by vector measures. We use stochastic vector measures as controls adapted to an increasing family of complete sigma algebras and prove the existence of optimal controls.
Optimal control of linear bottleneck problems
Optimal control of linear bottleneck problems
The regularity of Lagrange multipliers for state-constrained optimal control problems belongs to the basic questions of control theory. Here, we investigate bottleneck problems arising from optimal control problems for PDEs with certain mixed control-state inequality constraints. We show how to obtain Lagrange multipliers in Lp spaces for linear problems and give an application to linear parabolic optimal control problems.
Optimal control of linear impulsive antiperiodic boundary value problem on infinite dimensional spaces.
Optimal control of linearized compressible Navier–Stokes equations
We study an optimal boundary control problem for the two dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle. The control acts through the Dirichlet boundary condition. We first establish the existence and uniqueness of the solution for the two-dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle with inhomogeneous Dirichlet boundary data, not necessarily smooth. Then, we prove the existence and uniqueness of the optimal solution over...
Optimal control of nonlinear delay systems with implicit derivative and quadratic performance
The existence of optimal control for nonlinear delay systems having an implicit derivative with quadratic performance criteria is proved. The results are established by an iterative technique and using the Darbo fixed point theorem.
Optimal control of nonlinear evolution equations
In this paper, first we consider parametric control systems driven by nonlinear evolution equations defined on an evolution triple of spaces. The parametres are time-varying probability measures (Young measures) defined on a compact metric space. The appropriate optimization problem is a minimax control problem, in which the system analyst minimizes the maximum cost (risk). Under general hypotheses on the data we establish the existence of optimal controls. Then we pass to nonparametric...
Optimal control of nonlinear evolution equations associated with time-dependent subdifferentials and applications
In this paper we consider optimal control problems for abstract nonlinear evolution equations associated with time-dependent subdifferentials in a real Hilbert space. We prove the existence of an optimal control that minimizes the nonlinear cost functional. Also, we study approximating control problems of our equations. Then, we show the relationship between the original optimal control problem and the approximating ones. Moreover, we give some applications of our abstract results.
Optimal control of nonlinear one-dimensional periodic wave equation with x-dependent coefficients
This paper is concerned with an optimal control problem governed by the nonlinear one dimensional periodic wave equation with x-dependent coefficients. The control of the system is realized via the outer function of the state. Such a model arises from the propagation of seismic waves in a nonisotropic medium. By investigating some important properties of the linear operator associated with the state equation, we obtain the existence and regularity of the weak solution to the state equation. Furthermore,...
Optimal control of nonlinear second order evolution equations.