Adjoint differential inclusions in necessary conditions for the minimal trajectories of differential inclusions
Admissible relaxation in optimal control problems for infinite dimensional uncertain systems.
Algorithm for solving a generalized mixed equilibrium problem with perturbation in a Banach space.
An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator...
An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator...
An a priori Campanato type regularity condition for local minimisers in the calculus of variations
An a priori Campanato type regularity condition is established for a class of W1X local minimisers of the general variational integral where is an open bounded domain, F is of class C2, F is strongly quasi-convex and satisfies the growth condition for a p > 1 and where the corresponding Banach spaces X are the Morrey-Campanato space , µ < n, Campanato space and the space of bounded mean oscillation . The admissible maps are of Sobolev class W1,p, satisfying a Dirichlet boundary...
An application of conjugate duality for numerical solution of continuous convex optimal control problems
An approximation method in stochastic optimization and control
An approximation to discrete optimal feedback controls.
An estimation of the controllability time for single-input systems on compact Lie Groups
Geometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters...
An existence and uniqueness result for semilinear equations with Lipschitz nonlinearity.
An existence result for a nonconvex variational problem via regularity
Local Lipschitz continuity of minimizers of certain integrals of the Calculus of Variations is obtained when the integrands are convex with respect to the gradient variable, but are not necessarily uniformly convex. In turn, these regularity results entail existence of minimizers of variational problems with non-homogeneous integrands nonconvex with respect to the gradient variable. The -dependence, explicitly appearing in the integrands, adds significant technical difficulties in the proof.
An existence result for a nonconvex variational problem via regularity
Local Lipschitz continuity of minimizers of certain integrals of the Calculus of Variations is obtained when the integrands are convex with respect to the gradient variable, but are not necessarily uniformly convex. In turn, these regularity results entail existence of minimizers of variational problems with non-homogeneous integrands nonconvex with respect to the gradient variable. The x-dependence, explicitly appearing in the integrands, adds significant technical difficulties in the proof.
An extension of Fan's fixed point theorem and equilibrium point of an abstract economy
An implicit-function theorem for a class of monotone generalized equations
An instantaneous semi-Lagrangian approach for boundary control of a melting problem
In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on the characteristics method. The resulting time independent control problems are formulated as function space optimization problems with complementarity constraints. At each time step, the existence of an optimal solution is proved and first-order optimality conditions...
An observability estimate for parabolic equations from a measurable set in time and its applications
This paper presents a new observability estimate for parabolic equations in , where is a convex domain. The observation region is restricted over a product set of an open nonempty subset of and a subset of positive measure in . This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property for norm and time optimal control problems are provided.
An optimal control approach to cancer treatment under immunological activity
Mathematical models for cancer treatment that include immunological activity are considered as an optimal control problem with an objective that is motivated by a separatrix of the uncontrolled system. For various growth models on the cancer cells the existence and optimality of singular controls is investigated. For a Gompertzian growth function a synthesis of controls that move the state into the region of attraction of a benign equilibrium point is developed.
An optimal control problem for a generalized Boussinesq model: The time dependent case.
An optimal control problem for Helmholtz equation with non-local boundary conditions and quadratic funtional