Consensus for switched networks with unknown but bounded disturbances

We consider stationary consensus protocols for networks of dynamic agents with switching topologies. The measure of the neighbors' state is affected by Unknown But Bounded disturbances. Here the main contribution is the formulation and solution of what we call the $\epsilon$-consensus problem, where the states are required to converge in a tube of ray $\epsilon$ asymptotically or in finite time.Comment: 18 pages, 3 figures. The manuscript has been submitted for the Special issue on Control and optimization in Cooperative Networks. Submitted to SIAM SICO

Allocating Air Traffic Flow Management Slots

In Europe, when an imbalance between demand and capacity is detected for air traffic network resources, Air Traffic Flow Management slots are allocated to flights on the basis of a First Planned First Served principle. We propose a market mechanism to allocate such slots in the case of a single constrained en-route sector or airport. We show that our mechanism provides a slot allocation which is economically preferable to the current one as it enables airlines to pay for delay reduction or receive compensations for delay increases. We also discuss the implementation of our mechanism through two alternative distributed approaches that spare airlines the disclosure of private information. Both these approaches have the additional advantage that they directly involve airlines in the decision making process. Two computational examples relying on real data illustrate our findings.Air Transportation, Market Mechanism Design, Air Traffic Flow Management slots, Collaborative Decision Making, SESAR.

Airport slot allocation in Europe: economic efficiency and fairness

We propose a mechanism for solving the airport slot allocation problem in Europe. We consider the interdependence of the slots at different airports, and we maximize the efficiency of the system. Through an experimental analysis we quantitatively assess the cost imposed by grandfather rights, which constitute one of the main principles of the current slot allocation mechanism. Moreover, we introduce the possibility to fairly redistribute costs among airlines through monetary compensations. Our results suggest that it is possible to remove grandfather rights without significantly penalizing airlines.Air Traffic Management; Airport slot allocation; Compensation mechanism; SESAR.

Metaheuristic algorithms for the simultaneous slot allocation problem

In this paper, we formalize the simultaneous slot allocation problem. It is an extension of the problem currently tackled for allocating airport slots: it deals with all airports simultaneously and it enforces the respect of airspace sector capacities. By solving this novel problem, the system may overcome some major inefficiencies that characterize the current slot allocation process. We tackle the simultaneous slot allocation problem with two algorithms based on metaheuristics, namely Iterated Local Search and Variable Neighborhood Search, and with an integer linear programming model: for each of these three algorithms, we allow a fixed computation time, and we take the best solution found during that time as the final solution. We compare these algorithms on randomly generated instances, and we show that, when small instances are to be tackled, metaheuristics are competitive with the exact model. When medium or large instances are to be tackled, the exact model suffers some major issues in terms of memory and computation time requirements. Metaheuristics, instead, can deal with very large instances, achieving very high quality results.Air Traffic Management; Airport slot allocation; Metaheuristics; Integer linear programming

An integer programming formulation to allocate series of slots on an airport network

Several authors have introduced mathematical formulations for the airport slot allocation process, and the initial allocation in particular. They mostly replicate the current IATA process, performed on an airport-by- airport basis. However, airports are part of a network. The initial slot allocation should therefore be performed simultaneously at all airports, accounting for flight times to link departures and arrivals. [1] proposes an integer programming formulation to allocate a set of single-day slots on a network of airports. Extending that formulation, this paper additionally models the IATA rule stating that series rather than individual slots are to be allocated. A series of slots includes at least 5 slots at the same time and day-of-the-week, distributed regularly in a season. The objective of the allocation is to minimise airline costs due to the non-allocation of series of slots, their temporal displacement, and the deviation from the requested block or turnaround time for slots of coupled series. Preliminary experiments are based on a network of 152 European airports and consider about 300000 slot requests for seven Fridays of the 2017 summer season. Results quantify the increase of airline costs as a function of congestion. [1] Pellegrini P, Bolic T, Castelli L, Pesenti R, 2017. SOSTA: An effective model for the simultaneous optimisation of airport slot allocation. Transportation Research Part E: Logistics and Transportation Review 99:34-53

A comparison among Reinforcement Learning algorithms in financial trading systems

In this work we analyze and implement different Reinforcement Learning (RL) algorithms in financial trading system applications. RL-based algorithms applied to financial systems aim to find an optimal policy, that is an optimal mapping between the variables describing the state of the system and the actions available to an agent, by interacting with the system itself in order to maximize a cumulative return. In this contribution we compare the results obtained considering different on-policy (SARSA) and off-policy (Q-Learning, Greedy-GQ) RL algorithms applied to daily trading in the Italian stock market. We consider both computational issues related to the implementation of the algorithms, and issues originating from practical application to real stock markets, in an effort to improve previous results while keeping a simple and understandable structure of the used models

A threshold mechanism ensures minimum-path flow in lightning discharge

A well-known property of linear resistive electrical networks is that the current distribution minimizes the total dissipated power. When the circuit includes resistors with nonlinear monotonic characteristic, the current distribution minimizes in general a diferent functional. We show that, if the nonlinear characteristic is a threshold-like function and the current generator is concentrated in a single point, as in the case of lightning or dielectric discharge, then the current flow is concentrated along a single path, which is a minimum path to the ground with respect to the threshold. We also propose a dynamic model that explains and qualitatively reproduces the lightning transient behavior: initial generation of several plasma branches and subsequent dismissal of all branches but the one reaching the ground frst, which is the optimal one

Optimal control of the mean field game equilibrium for a pedestrian tourists' flow model

Art heritage cities are popular tourist destinations but for many of them overcrowding is becoming an issue. In this paper, we address the problem of modeling and analytically studying the flow of tourists along the narrow alleys of the historic center of a heritage city. We initially present a mean field game model, where both continuous and switching decisional variables are introduced to respectively describe the position of a tourist and the point of interest that it may visit. We prove the existence of a mean field game equilibrium. A mean field game equilibrium is Nash-type equilibrium in the case of infinitely many players. Then, we study an optimization problem for an external controller who aims to induce a suitable mean field game equilibrium

Parameter space exploration within dynamic simulations of signaling networks

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Robust control strategies for multi-inventory systems with average flow constraints.

In this paper, we consider multi-inventory systems in the presence of uncertain demand. We assume that (i) demand is unknown but bounded in an assigned compact set and (ii) the control inputs (controlled flows) are subject to assigned constraints. Given a long-term average demand, we select a nominal flow that feeds such a demand. In this context, we are interested in a control strategy that meets at each time all possible current demands and achieves the nominal flow in the average. We provide necessary and sufficient conditions for such a strategy to exist and we characterize the set of achievable flows. Such conditions are based on linear programming and thus they are constructive. In the special case of a static flow (i.e. a system with 0-capacity buffers) we show that the strategy must be affine. The dynamic problem can be solved by a linear-saturated control strategy (inspired by the previous one). We provide numerical analysis and illustrative examples