In this paper we will present an adaptive wavelet scheme to solvethe generalized Stokes problem. Using divergence free wavelets, theproblem is transformed into an equivalent matrix vector system, thatleads to a positive definite system of reduced size for thevelocity. This system is solved iteratively, where the applicationof the infinite stiffness matrix, that is sufficiently compressible,is r...

Abstract. This paper is devoted to present a method of proving verification theorems for stochastic optimal control of finite dimensional diffusion processes without control in the diffusion term. The value function is assumed to be continuous in time and once differentiable in the space variable (C) instead of once differentiable in time and twice in space (C), like in the classical results. T...

This work is devoted to distributed optimal control problems for time-periodic eddy current problems. We apply the multiharmonic approach to the optimality system and construct a new preconditioned MinRes solver for the system of frequency domain equations. We show that this solver is robust with respect to the space discretization and time discretization parameters as well as all involved “bad...

We study an optimal control problem arising from a generalization of rockpaper-scissors in which the number of strategies may be selected from any positive odd number greater than 1 and in which the payoff to the winner is controlled by a control variable γ. Using the replicator dynamics as the equations of motion, we show that a quasi-linearization of the problem admits a special optimal contr...

where Ω ⊂ RN , N = 2, 3 is a bounded domain with C0,1-boundary, ν > 0 is a fixed number, yd and yc are given functions from L2(Ω). Furthermore, ua and ub are given real numbers with ua < ub. The difficulty of low regularity of solutions of problems with pointwise state constraints is pointed out in (1). Therefore, different regularization concepts are developed, see e.g. (2), (3), (4) and (5). ...

In this paper, the general formulation of periodically time-varying state-feedback controllers with memory is considered for the first time. New analysis and synthesis conditions for robust stability are proposed. The flexibility of these new results allows the user to freely add degrees-of-freedom to the control law which appears to effectively reduce the conservatism of the synthesis conditio...

Repetitive processes are a distinct class of 2D systems of both theoretical and practical interest. The stability theory for these processes currently consists of two distinct concepts termed asymptotic stability and stability along the pass respectively where the former is a necessary condition for the latter. Recently applications have arisen where asymptotic stability is too weak and stabili...

We introduce the rigorous limit process connecting finite dimensional sparse optimal control problems with ODE constraints, modelling parsimonious interventions on the dynamics of a moving population divided into leaders and followers, to an infinite dimensional optimal control problem with a constraint given by a system of ODE for the leaders coupled with a PDE of Vlasov-type, governing the dy...

The problem of many hypotheses logarithmically asymptotically optimal (LAO) testing for a model consisting of three or more independent objects is solved. It is supposed that M probability distributions are known and each object independently of others follows to one of them. The matrix of asymptotic interdependencies (reliability– reliability functions) of all possible pairs of the error proba...