Model categories for orthogonal calculus

We restate the notion of orthogonal calculus in terms of model categories. This provides a cleaner set of results and makes the role of O(n)-equivariance clearer. Thus we develop model structures for the category of n-polynomial and n-homogeneous functors, along with Quillen pairs relating them. We then classify n-homogeneous functors, via a zig-zag of Quillen equivalences, in terms of spectra with an O(n)-action. This improves upon the classification theorem of Weiss. As an application, we develop a variant of orthogonal calculus by replacing topological spaces with orthogonal spectra.

D3.1 Benefits Analysis of the Initial Operational Cruiser-Feeder Concept

The REsearch on a CRuiser Enabled Air Transport Environment (RECREATE) project is considers the introduction and airworthiness of cruiser-feeder operations for civil aircraft. Cruiser-feeder operations are investigated as a promising pioneering idea for the air transport of the future. The soundness of the concept of cruiser-feeder operations for civil aircraft can be understood, taking air-to-air refueling operations as an example. For this example, a comprehensive estimate of the benefits can be made, which shows a fuel burn reduction potential and a CO2 emission reduction of 31% for a typical 6000 nautical miles flight with a payload of 250 passengers. This reduction potential is known to be large by any standard. The top level objective of the RECREATE project is to demonstrate on a preliminary design level that cruiser-feeder operations (as a concept to reduce fuel burn and CO2 emission levels) can be shown to comply with the airworthiness requirements for civil aircraft. The underlying Scientific and Technological (S&T) objectives are to determine and study airworthy operational concepts for cruiser-feeder operations, and to derive and quantify benefits in terms of CO2 emission reduction but also other benefits.

Work Package (WP) 3 has the objective to substantiate the assumed benefits of the cruiser/feeder operations through refined analysis and simulation. In this report, initial benefits evaluation of the initial RECREATE cruiser/feeder concepts is presented. The benefits analysis is conducted in delta mode, i.e. comparison is made with a baseline system. Since comparing different aircraft and air transport systems is never a trivial task, appropriate measures and metrics are defined and selected first. Non-dimensional parameters are defined and values for the baseline system derived.

The impact of cruiser/feeder operations such as air-to-air refueling are studied with respect to fuel-burn (or carbon-dioxide), noise and congestion. For this purpose, traffic simulations have been conducted.
Cruiser/feeder operations will have an impact on dispatch reliability as well. An initial assessment of the effect on dispatch reliability has been made and is reported.

Finally, a considerable effort has been made to create the infrastructure for economic delta analysis of the cruiser/feeder concept of operation. First results of the cost analysis have been obtained.

D1.2 Operational Cruiser-Feeder Concept

The project REsearch on a CRuiser Enabled Air Transport Environment (RECREATE) is about the introduction and airworthiness of cruiser-feeder operations for civil aircraft. Cruiser-feeder operations are investigated as a promising pioneering idea for the air transport of the future.
The top level objective of the project is to demonstrate on a preliminary design level that cruiser-feeder operations (as a concept to reduce fuel burn and CO2 emission levels) can be shown to comply with the airworthiness requirements for civil aircraft. The project is funded through the Seventh Framework Programme of the European Commission. Work Package (WP) 1 has the objective to substantiate that viable and acceptable concepts for cruiser/feeder operations exist. In this deliverable the initial operational concept of the RECREATE cruiser/feeder is presented.

Can(Plan)+: Extending the Operational Semantics of the BDI Architecture to deal with Uncertain Information

The BDI architecture, where agents are modelled based on their beliefs, desires and intentions, provides a practical approach to develop large scale systems. However, it is not well suited to model complex Supervisory Control And Data Acquisition (SCADA) systems pervaded by uncertainty. In this paper we address this issue by extending the operational semantics of Can(Plan) into Can(Plan)+. We start by modelling the beliefs of an agent as a set of epistemic states where each state, possibly using a different representation, models part of the agent's beliefs. These epistemic states are stratified to make them commensurable and to reason about the uncertain beliefs of the agent. The syntax and semantics of a BDI agent are extended accordingly and we identify fragments with computationally efficient semantics. Finally, we examine how primitive actions are affected by uncertainty and we define an appropriate form of lookahead planning.

Belief change with noisy sensing in the situation calculus

Situation calculus has been applied widely in arti?cial intelligence to model and reason about actions and changes in dynamic systems. Since actions carried out by agents will cause constant changes of the agents’ beliefs, how to manage
these changes is a very important issue. Shapiro et al. [22] is one of the studies that considered this issue. However, in this framework, the problem of noisy sensing, which often presents in real-world applications, is not considered. As a
consequence, noisy sensing actions in this framework will lead to an agent facing inconsistent situation and subsequently the agent cannot proceed further. In this paper, we investigate how noisy sensing actions can be handled in iterated
belief change within the situation calculus formalism. We extend the framework proposed in [22] with the capability of managing noisy sensings. We demonstrate that an agent can still detect the actual situation when the ratio of noisy sensing actions vs. accurate sensing actions is limited. We prove that our framework subsumes the iterated belief change strategy in [22] when all sensing actions are accurate. Furthermore, we prove that our framework can adequately handle belief introspection, mistaken beliefs, belief revision and belief update even with noisy sensing, as done in [22] with accurate sensing actions only.

Calculus of variations on time scales and discrete fractional calculus

Estudamos problemas do cálculo das variações e controlo óptimo no contexto das escalas temporais. Especificamente, obtemos condições necessárias de optimalidade do tipo de Euler–Lagrange tanto para lagrangianos dependendo de derivadas delta de ordem superior como para problemas isoperimétricos. Desenvolvemos também alguns métodos directos que permitem resolver determinadas classes de problemas variacionais através de desigualdades em escalas temporais. No último capítulo apresentamos operadores de diferença fraccionários e propomos um novo cálculo das variações fraccionário em tempo discreto. Obtemos as correspondentes condições necessárias de Euler– Lagrange e Legendre, ilustrando depois a teoria com alguns exemplos.

Fractional calculus on time scales - Cálculo fraccional em escalas temporais

Introduzimos um cálculo das variações fraccional nas escalas temporais ℤ e (hℤ)!. Estabelecemos a primeira e a segunda condição necessária de optimalidade. São dados alguns exemplos numéricos que ilustram o uso quer da nova condição de Euler–Lagrange quer da nova condição do tipo de Legendre. Introduzimos também novas definições de derivada fraccional e de integral fraccional numa escala temporal com recurso à transformada inversa generalizada de Laplace.

Symmetric quantum calculus

Generalizamos o cálculo Hahn variacional para problemas do cálculo das variações que envolvem derivadas de ordem superior. Estudamos o cálculo quântico simétrico, nomeadamente o cálculo quântico alpha,beta-simétrico, q-simétrico e Hahn-simétrico. Introduzimos o cálculo quântico simétrico variacional e deduzimos equações do tipo Euler-Lagrange para o cálculo q-simétrico e Hahn simétrico. Definimos a derivada simétrica em escalas temporais e deduzimos algumas das suas propriedades. Finalmente, introduzimos e estudamos o integral diamond que generaliza o integral diamond-alpha das escalas temporais.

Computational methods in the fractional calculus of variations and optimal control

The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the lack of analytic methods to solve such fractional problems, numerical techniques are developed. Here, we mainly investigate the approximation of fractional operators by means of series of integer-order derivatives and generalized finite differences. We give upper bounds for the error of proposed approximations and study their efficiency. Direct and indirect methods in solving fractional variational problems are studied in detail. Furthermore, optimality conditions are discussed for different types of unconstrained and constrained variational problems and for fractional optimal control problems. The introduced numerical methods are employed to solve some illustrative examples.