Modelling, simulation and control of rotary-wing aircraft in multi-agent scenario

The topic of this thesis is the design and the implementation of mathematical models and control system algorithms for rotary-wing unmanned aerial vehicles to be used in cooperative scenarios. The use of rotorcrafts has many attractive advantages, since these vehicles have the capability to take-off and land vertically, to hover and to move backward and laterally. Rotary-wing aircraft missions require precise control characteristics due to their unstable and heavy coupling aspects. As a matter of fact, flight test is the most accurate way to evaluate flying qualities and to test control systems. However, it may be very expensive and/or not feasible in case of early stage design and prototyping. A good compromise is made by a preliminary assessment performed by means of simulations and a reduced flight testing campaign. Consequently, having an analytical framework represents an important stage for simulations and control algorithm design. In this work mathematical models for various helicopter configurations are implemented. Different flight control techniques for helicopters are presented with theoretical background and tested via simulations and experimental flight tests on a small-scale unmanned helicopter. The same platform is used also in a cooperative scenario with a rover. Control strategies, algorithms and their implementation to perform missions are presented for two main scenarios. One of the main contributions of this thesis is to propose a suitable control system made by a classical PID baseline controller augmented with L1 adaptive contribution. In addition a complete analytical framework and the study of the dynamics and the stability of a synch-rotor are provided. At last, the implementation of cooperative control strategies for two main scenarios that include a small-scale unmanned helicopter and a rover.

Multi-Principal Agency and the Compliance with Professional Guidelines in Health Systems: Economic and Regulatory Perspectives

Amid the trend of rising health expenditure in developed economies, changing the healthcare delivery models is an important point of action for service regulators to contain this trend. Such a change is mostly induced by either financial incentives or regulatory tools issued by the regulators and targeting service providers and patients. This creates a tripartite interaction between service regulators, professionals, and patients that manifests a multi-principal agent relationship, in which professionals are agents to two principals: regulators and patients. This thesis is concerned with such a multi-principal agent relationship in healthcare and attempts to investigate the determinants of the (non-)compliance to regulatory tools in light of this tripartite relationship. In addition, the thesis provides insights into the different institutional, economic, and regulatory settings, which govern the multi-principal agent relationship in healthcare in different countries. Furthermore, the thesis provides and empirically tests a conceptual framework of the possible determinants of (non-)compliance by physicians to regulatory tools issued by the regulator. The main findings of the thesis are first, in a multi-principal agent setting, the utilization of financial incentives to align the objectives of professionals and the regulator is important but not the only solution. This finding is based on the heterogeneity in the financial incentives provided to professionals in different health markets, which does not provide a one-size-fits-all model of financial incentives to influence clinical decisions. Second, soft law tools as clinical practice guidelines (CPGs) are important tools to mitigate the problems of the multi-principal agent setting in health markets as they reduce information asymmetries while preserving the autonomy of professionals. Third, CPGs are complex and heterogeneous and so are the determinants of (non-)compliance to them. Fourth, CPGs work but under conditions. Factors such as intra-professional competition between service providers or practitioners might lead to non-compliance to CPGs – if CPGs are likely to reduce the professional’s utility. Finally, different degrees of soft law mandate have different effects on providers’ compliance. Generally, the stronger the mandate, the stronger the compliance, however, even with a strong mandate, drivers such as intra-professional competition and co-management of patients by different professionals affected the (non-)compliance.

Incompressible limit and well-posedness of PDE models of tissue growth

Both compressible and incompressible porous medium models are used in the literature to describe the mechanical aspects of living tissues. Using a stiff pressure law, it is possible to build a link between these two different representations. In the incompressible limit, compressible models generate free boundary problems where saturation holds in the moving domain. Our work aims at investigating the stiff pressure limit of reaction-advection-porous medium equations motivated by tumor development. Our first study concerns the analysis and numerical simulation of a model including the effect of nutrients. A coupled system of equations describes the cell density and the nutrient concentration and the derivation of the pressure equation in the stiff limit was an open problem for which the strong compactness of the pressure gradient is needed. To establish it, we use two new ideas: an L3-version of the celebrated Aronson-Bénilan estimate, and a sharp uniform L4-bound on the pressure gradient. We further investigate the sharpness of this bound through a finite difference upwind scheme, which we prove to be stable and asymptotic preserving. Our second study is centered around porous medium equations including convective effects. We are able to extend the techniques developed for the nutrient case, hence finding the complementarity relation on the limit pressure. Moreover, we provide an estimate of the convergence rate at the incompressible limit. Finally, we study a multi-species system. In particular, we account for phenotypic heterogeneity, including a structured variable into the problem. In this case, a cross-(degenerate)-diffusion system describes the evolution of the phenotypic distributions. Adapting methods recently developed in the context of two-species systems, we prove existence of weak solutions and we pass to the incompressible limit. Furthermore, we prove new regularity results on the total pressure, which is related to the total density by a power law of state.

Vehicle routing and location routing problems with minimum latency: algorithms and models

Latency can be defined as the sum of the arrival times at the customers. Minimum latency problems are specially relevant in applications related to humanitarian logistics. This thesis presents algorithms for solving a family of vehicle routing problems with minimum latency. First the latency location routing problem (LLRP) is considered. It consists of determining the subset of depots to be opened, and the routes that a set of homogeneous capacitated vehicles must perform in order to visit a set of customers such that the sum of the demands of the customers assigned to each vehicle does not exceed the capacity of the vehicle. For solving this problem three metaheuristic algorithms combining simulated annealing and variable neighborhood descent, and an iterated local search (ILS) algorithm, are proposed. Furthermore, the multi-depot cumulative capacitated vehicle routing problem (MDCCVRP) and the multi-depot k-traveling repairman problem (MDk-TRP) are solved with the proposed ILS algorithm. The MDCCVRP is a special case of the LLRP in which all the depots can be opened, and the MDk-TRP is a special case of the MDCCVRP in which the capacity constraints are relaxed. Finally, a LLRP with stochastic travel times is studied. A two-stage stochastic programming model and a variable neighborhood search algorithm are proposed for solving the problem. Furthermore a sampling method is developed for tackling instances with an infinite number of scenarios. Extensive computational experiments show that the proposed methods are effective for solving the problems under study.