Time optimal control problem for differential inclusions
Time-dependent Stokes equations with measure data.
Time-optimal boundary control of a parabolic system with time lags given in integral form
In this paper, the time-optimal boundary control problem for a distributed parabolic system in which time lags appear in integral form in both the state equation and the boundary condition is presented. Some particular properties of optimal control are discussed.
Time-optimal boundary control of an infinite order parabolic system with time lags
In this paper the time-optimal boundary control problem is presented for a distributed infinite order parabolic system in which time lags appear in the integral form both in the state equation and in the boundary condition. Some specific properties of the optimal control are discussed.
Time-optimal control of a third-order plant
Time-optimal control of infinite order hyperbolic systems with time delays
In this paper, the time-optimal control problem for infinite order hyperbolic systems in which time delays appear in the integral form both in state equations and in boundary conditions is considered. Optimal controls are characterized in terms of an adjoint system and shown to be unique and bang-bang. These results extend to certain cases of nonlinear control problems. The particular properties of optimal control are discussed.
Time-optimal control of nonlinear parabolic systems with constrained derivative of control, existence theorem
Time-optimal control of systems with fractional dynamics.
Topological degree, Jacobian determinants and relaxation
A characterization of the total variation of the Jacobian determinant is obtained for some classes of functions outside the traditional regularity space . In particular, explicit formulas are deduced for functions that are locally Lipschitz continuous away from a given one point singularity . Relations between and the distributional determinant are established, and an integral representation is obtained for the relaxed energy of certain polyconvex functionals at maps .
Topological properties of a new graph topology.
Topology and geometry of nontrivial rank-one convex hulls for two-by-two matrices
Continuing earlier work by Székelyhidi, we describe the topological and geometric structure of so-called T4-configurations which are the most prominent examples of nontrivial rank-one convex hulls. It turns out that the structure of T4-configurations in is very rich; in particular, their collection is open as a subset of . Moreover a previously purely algebraic criterion is given a geometric interpretation. As a consequence, we sketch an improved algorithm to detect T4-configurations. ...
Topology optimization of systems governed by variational inequalities
This paper deals with the formulation of the necessary optimality condition for a topology optimization problem of an elastic body in unilateral contact with a rigid foundation. In the contact problem of Tresca, a given friction is governed by an elliptic variational inequality of the second order. The optimization problem consists in finding such topology of the domain occupied by the body that the normal contact stress along the contact boundary of the body is minimized. The topological derivative...
Transformation of optimal control problems of descriptor systems into problems with state-space systems
We show how we can transform the and control problems of descriptor systems with invariant zeros on the extended imaginary into problems with state-space systems without such zeros. Then we present necessary and sufficient conditions for existence of solutions of the original problems. Numerical algorithm for control is given, based on the Nevanlinna-Pick theorem. Also, we present an explicit formula for the optimal controller.
Translation invariant spaces and asymptotic properties of variational equations.
Traveling waves in a cylinder rolling on a flat surface
Turnpike properties of approximate solutions of autonomous variational problems
Turnpike theorem for convex infinite dimensional discrete-time control systems.
Two dimensional optimal transportation problem for a distance cost with a convex constraint
We first prove existence and uniqueness of optimal transportation maps for the Monge’s problem associated to a cost function with a strictly convex constraint in the Euclidean plane ℝ2. The cost function coincides with the Euclidean distance if the displacement y − x belongs to a given strictly convex set, and it is infinite otherwise. Secondly, we give a sufficient condition for existence and uniqueness of optimal transportation maps for the original Monge’s problem in ℝ2. Finally, we get existence...
Two Dimensional Variational Problems with Thin Obstacles.
Two generalizations of Komlós' theorem with lower closure-type applications.