We consider semi{discrete approximations of optimal control problems for linear distributed parameter dynamical systems, with cost functionals in Bolza or innnite horizon form. We give conditions for the convergence of approximate value functions and prove that the approximate optimal controls are a minimizing sequence for the continuous problem. We also show some concrete applications.

‎Semidiscrete finite element approximation of a hyperbolic type‎ ‎integro-differential equation is studied. The model problem is‎ ‎treated as the wave equation which is perturbed with a memory term.‎ ‎Stability estimates are obtained for a slightly more general problem.‎ ‎These, based on energy method, are used to prove optimal order‎ ‎a priori error estimates.‎

In this survey, receding horizon control is presented as a method for obtaining approximately optimal solutions to infinite horizon optimal control problems by iteratively solving a sequence of finite horizon optimal control problems. We investigate conditions under which we can obtain mathematically rigorous approximation results for this approach. A key ingredient of our analysis is the so-ca...

The asymptotic behavior of the n{widths of multiplier operators from Lp0;1] into Lq0;1] is studied. General upper and lower bounds for the n{widths in terms of the multipliers are established. Moreover, it is shown that these upper and lower bounds coincide for some important concrete examples.

‎In this paper‎, ‎we study spectral element approximation for a constrained‎ ‎optimal control problem in one dimension‎. ‎The equivalent a posteriori error estimators are derived for‎ ‎the control‎, ‎the state and the adjoint state approximation‎. ‎Such estimators can be used to‎ ‎construct adaptive spectral elements for the control problems.

Local adaptive grid refinement is an important technique in finite element methods. Its study can be traced back to the pioneering work [2] in one dimension. In recent years, mathematicians start to prove the convergence and optimal complexity of the adaptive procedure in multi-dimensions. [11] first proved an error reduction in the energy norm for the Poisson equation provided the initial mesh...

We consider a model of a nancial corporation which has to nd an optimal policy balancing its risk and expected proots. The example treated in this paper is related to an insurance company with the risk control method known in the industry as excess-of-loss reinsurance. Under this scheme the insurance company divert part of its premium stream to another company in exchange of an obligation to pi...

The general theory of approximation of (possibly generalized) Young measures is presented, and concrete cases are investigated. An adjoint-operator approach, combined with quasi-interpolation of test integrands, is systematically used. Applicability is demonstrated on an optimal control problem for an elliptic system, together with 1-dimensional illustrative calculations of various options.

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