Optimal control of a system governed by Petrowsky type equation with an infinite number of variables
Optimal control of a waste water cleaning plant.
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 combined therapy in a single strain HIV-1 model.
Optimal control of delay-differential inclusions with multivalued initial conditions in infinite dimensions
Optimal control of ∞-dimensional stochastic systems via generalized solutions of HJB equations
In this paper, we consider optimal feedback control for stochastc infinite dimensional systems. We present some new results on the solution of associated HJB equations in infinite dimensional Hilbert spaces. In the process, we have also developed some new mathematical tools involving distributions on Hilbert spaces which may have many other interesting applications in other fields. We conclude with an application to optimal stationary feedback control.
Optimal control of dynamical processes in two-phase systems of solid-liquid type
Optimal control of electromagnetic energy.
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 linear impulsive antiperiodic boundary value problem on infinite dimensional spaces.
Optimal control of linear stochastic evolution equations in Hilbert spaces and uniform observability
In this paper we study the existence of the optimal (minimizing) control for a tracking problem, as well as a quadratic cost problem subject to linear stochastic evolution equations with unbounded coefficients in the drift. The backward differential Riccati equation (BDRE) associated with these problems (see [chen], for finite dimensional stochastic equations or [UC], for infinite dimensional equations with bounded coefficients) is in general different from the conventional BDRE (see [1990], [ukl])....
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 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 nonsmooth system governed by quasi-linear elliptic equations.
Optimal control of non-well-posed distributed systems
Optimal control of obstacle problems : existence of Lagrange multipliers
Optimal Control of Obstacle Problems: Existence of Lagrange Multipliers
We study first order optimality systems for the control of a system governed by a variational inequality and deal with Lagrange multipliers: is it possible to associate to each pointwise constraint a multiplier to get a “good” optimality system? We give positive and negative answers for the finite and infinite dimensional cases. These results are compared with the previous ones got by penalization or differentiation.
Optimal control of partial differential equations with affine control constraints
Optimal control of quasilinear elliptic equations with non differentiable coefficients at the origin.
In this paper we study some optimal control problems of systems governed by quasilinear elliptic equations in divergence form with non differentiable coefficients at the origin. We prove existence of solutions and derive the optimality conditions by considering a perturbation of the differential operator coefficients that removes the singularity at the origin. Regularity of optimal controls is also deduced.