A shooting algorithm for problems with singular arcs

In this article we propose a shooting algorithm for a class of optimal control problems for which all control variables appear linearly. The shooting system has, in the general case, more equations than unknowns and the Gauss-Newton method is used to compute a zero of the shooting function. This shooting algorithm is locally quadratically convergent if the derivative of the shooting function is one-to-one at the solution. The main result of this paper is to show that the latter holds whenever a sufficient condition for weak optimality is satisfied. We note that this condition is very close to a second order necessary condition. For the case when the shooting system can be reduced to one having the same number of unknowns and equations (square system) we prove that the mentioned sufficient condition guarantees the stability of the optimal solution under small perturbations and the invertibility of the Jacobian matrix of the shooting function associated to the perturbed problem. We present numerical tests that validate our method.Comment: No. RR-7763 (2011); Journal of Optimization, Theory and Applications, published as 'Online first', January 201

Soil vs. glass: an integrated approach towards the characterization of soil as a burial environment for the glassware of Cucagna Castle (Friuli, Italy)

This research is performed on a selection of archaeological glass finds with corresponding soil samples, excavated on the site of the High Medieval castle Cucagna in Friuli/Northern Italy. In the frame of understanding medieval glass technology and the chemical-physical conditions that influenced the state of preservation of the glass finds, this study uses a multi-analytical line-up of methods to characterize the composition of the glass and basic parameters of the soil including texture, mineralogical composition, pH, redox potential (Eh) and electric conductivity (EC). The results show that glass corrosion in soil not only depends on acidity, alkalinity or glass composition but also on the texture of the soil, measurable as grain-size distribution, and the mineralogical composition. The compositional groups of the glassware from Cucagna indicate the use of various raw material sources, pointing to Northern and Central Italian glass workshops with primary or secondary glass production.[GRAPHICS].FdA – Publicaties zonder aanstelling Universiteit Leide

Global Biodiversity and Phylogenetic Evaluation of Remipedia (Crustacea)

Remipedia is one of the most recently discovered classes of crustaceans, first described in 1981 from anchialine caves in the Bahamas Archipelago. The class is divided into the order Enantiopoda, represented by two fossil species, and Nectiopoda, which contains all known extant remipedes. Since their discovery, the number of nectiopodan species has increased to 24, half of which were described during the last decade. Nectiopoda exhibit a disjunct global distribution pattern, with the highest abundance and diversity in the Caribbean region, and isolated species in the Canary Islands and in Western Australia. Our review of Remipedia provides an overview of their ecological characteristics, including a detailed list of all anchialine marine caves, from which species have been recorded. We discuss alternative hypotheses of the phylogenetic position of Remipedia within Arthropoda, and present first results of an ongoing molecular-phylogenetic analysis that do not support the monophyly of several nectiopodan taxa. We believe that a taxonomic revision of Remipedia is absolutely essential, and that a comprehensive revision should include a reappraisal of the fossil record

The shooting approach in analyzing bang-bang extremals with simultaneous control switches

The paper is devoted to stability investigation of optimal structure and switching points position for parametric bang-bang control problem with special focus on simultaneous switches of two control components. In contrast to problems where only simple switches occur, the switching points in general are no longer differentiable functions of input parameters. Conditions for Lipschitz stability are found which generalize known sufficient optimality conditions to nonsmooth situation. The analysis makes use of backward shooting representation of extremals, and of generalized implicit function theorems. The Lipschitz properties are illustrated for an example by constructing backward parameterized family of extremals and providing first-order switching points prediction

Optimality properties of controls with bang-bang components in problems with semilinear state equation

In this paper we study optimal control problems with bang-bang solution behavior for a special class of semilinear dynamics. Generalizing a former result for linear systems, optimlity conditions are derived by a duality based approach. The results apply for scalar as well as for vector control functions and, in particular, for the case of the so-called multiple switches, too. Further, an iterative procedure for determining switching points is proposed, and convergence results are provided

Stability analysis of variational inequalities for bang-singular-bang controls

The paper is related to parameter dependent optimal control problems for control-affine systems. The case of scalar reference control with bang-singular-bang structure is considered. The analysis starts from a variational inequality (VI) formulation of Pontryagin’s Maximum Principle. In a first step, under appropriate higher-order sufficient optimality conditions, the existence of solutions for the linearized problem (LVI) is proven. In a second step, for a certain class of right-hand side perturbation, it is show that the controls from LVI have bang-singular-bang structure and, in L1 topology, depend Lipschitz continuously on the data. Applying finally a common fixed-point approach to VI, the results are brought together to obtain existence and structural stability results for extremals of the original control problem under parameter perturbation