Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity

The main focus of this paper is to develop a sufficiency criterion for optimality in nonlinear optimal control problems defined on time scales. In particular, it is shown that the coercivity of the second variation together with the controllability of the linearized dynamic system are sufficient for the weak local minimality. The method employed is based on a direct approach using the structure of this optimal control problem. The second aim pertains to the sensitivity analysis for parametric control problems defined on time scales with separately varying state endpoints. Assuming a slight strengthening of the sufficiency criterion at a base value of the parameter, the perturbed problem is shown to have a weak local minimum and the corresponding multipliers are shown to be continuously differentiable with respect to the parameter. A link is established between (i) a modification of the shooting method for solving the associated boundary value problem, and (ii) the sufficient conditions involving the coercivity of the accessory problem, as opposed to the Riccati equation, which is also used for this task. This link is new even for the continuous time setting.

Las consecuencias de la reforma del art. 135.2 del Reglamento del Parlamento de Cataluña para aprobar la Ley de referéndum y la de transitoriedad jurídica: suspensión y STC 139/2017

LABURPENA: Ikerketa-lan honek xede du Kataluniako Parlamentuaren araudiko 135.2. artikuluaren erreforma aztertzea. Erreforma horren bidez, zera ezarri zen: ahobatezkotasuna ez dela beharrezkoa lege-proposamenak irakurketa bakarreko prozeduraren bitartez aurkezteko, eta isiltasuna gorde da prozedura beraren baitan zuzenketak egiteko aukerari buruz. Izan ere, erreforma hori zela-eta, konstituzio-kontrakotasuneko errekurtsoa aurkeztu zen, EKren 23.2. artikulua urratzen zuelakoan, eta Konstituzio Auzitegiaren 139/2017 Epaiak parlamentuaren araudi batean baino gehiagotan eragina izan duenez gero, benetako leading case bat bihurtu da. Beraz, egoera hori aztertzeak ahalbidetzen du doktrina bat sendotzen joatea, erabaki ahal izateko lege-proposamenak irakurketa bakarreko prozeduraren bitartez izapidetzerakoan ahobatezkotasun eza eta prozedura beraren baitan zuzenketak egiteko aukerari buruz isiltasuna gordetzea uztartzea Konstituzioaren araberakoa den edo, aldiz, konstituzioaren kontra egiten duen. Bestalde, gatazka osagarri gisa, Kataluniako Parlamentuaren araudiaren erreforma abiatzeko prozeduraren aurka aurkeztu eta onartu ez zen babes-errekurtsoa ere aztertu egin du. RESUMEN: La presente investigación trata de analizar aquella reforma del Art. 135.2 del Reglamento del Parlamento de Cataluña mediante la cual se eliminó la unanimidad para presentar proposiciones de ley por lectura única y se guardó silencio sobre la posibilidad de realizar enmiendas en el interior del mismo procedimiento, cuestión por la cual se presentó un recurso de inconstitucionalidad por supuesta vulneración del Art. 23.2 CE que, al afectar a más de un reglamento parlamentario, ha convertido el fallo de la STC 139/2017 en un verdadero leading case cuyo estudio permite ir consolidando una doctrina sobre la constitucionalidad o no de compaginar la ausencia de unanimidad para la tramitación de las proposiciones de ley por lectura única con el silencio sobre la posibilidad de presentar enmiendas en su interior. Asimismo, como problemática accesoria, también se analiza el inadmitido recurso de amparo contra el procedimiento utilizado para iniciar la reforma del Reglamento del Parlamento catalán. ABSTRACT: The present investigation seeks to analyze that reform of the Art. 135.2 of the standing orders of the Parliament of Catalonia by means of which the unanimity was eliminated to submit legislative proposals by single reading and kept silence on the possibility of making amendments within the same procedure, issue for which an appeal of unconstitutionality was filed for alleged violation of Art. 23.2 of the Constitution, that, by affecting more than one parliamentary standing order, has made judgment STC 139/2017 a true leading case whose study allows us to consolidate a doctrine on the constitutionality or not of combining the absence of unanimity for the processing of the legislative proposals by single reading with the silence regarding the possibility of tabling amendments on them. Likewise, as an accessory problem, it is also analyzed the rejected amparo against the procedure used to initiate the reform of the standing orders of the Parliament of Catalonia.

Low Cost Short Life Gas Turbine Design

Results of low cost gas turbine engine design studies are presented. System requirements are discussed and their effects on engine design and cost are analyzed. Parametric performance data are presented and the use of these data in engine build cost trades is discussed. The evolution of specific component fabrication techniques on selected components is discussed, and the overall effect on the engine cost is analyzed and described. The technique of achieving low manufacturing costs by the use of innovative design, keyed to operational requirements rather than new processes, is described. The accessory problem is discussed and a potentially low cost fuel control concept described. A cross section drawing of a simple production turbojet is shown and the use of a technique for low cost design is outlined.