2,298 research outputs found
State Feedback Optimal Control with Singular Solution for a Class of Nonlinear Dynamics
The paper studies the problem of determining the optimal control when singular arcs are present in the solution.
In the general classical approach the expressions obtained depend on the state and the costate variables at the
same time, so requiring a forward-backward integration for the computation of the control. In this paper,
sufficient conditions on the dynamics structure are provided and discussed in order to have both the control
and the switching function depending on the state only, so simplifying the computation avoiding the necessity
of the backward integration. The approach has been validated on a classical SIR epidemic model
Spreading processes in Multilayer Networks
Several systems can be modeled as sets of interconnected networks or networks
with multiple types of connections, here generally called multilayer networks.
Spreading processes such as information propagation among users of an online
social networks, or the diffusion of pathogens among individuals through their
contact network, are fundamental phenomena occurring in these networks.
However, while information diffusion in single networks has received
considerable attention from various disciplines for over a decade, spreading
processes in multilayer networks is still a young research area presenting many
challenging research issues. In this paper we review the main models, results
and applications of multilayer spreading processes and discuss some promising
research directions.Comment: 21 pages, 3 figures, 4 table
Analysis, Simulation and Control of a New Measles Epidemic Model
In this paper the problem of modeling and controlling the measles epidemic spread is faced. A new model
is proposed and analysed; besides the categories usually considered in measles modeling, the susceptible,
the exposed, the infected, the removed and, less frequently, the quarantine individuals, two new categories
are herein introduced: the immunosuppressed subjects, that can not be vaccinated, and the patients with an
additional complication, not risky by itself but dangerous if caught togeter with the measles. These two
novelties are taken into account in designing and scheduling suitably control actions such as vaccination,
whenever possible, prevention, quarantine and treatment, when limited resources are available. An analysis of
the model is developed and the optimal control strategies are compared with other not optimized actions. By
using the Pontryagin principle, it is shown the prevailing role of the vaccination in guaranteeing the protection
to immunosuppressed individuals, as well as the importance of a prompt response of the society when an
epidemic spread occurs, such as the quarantine intervention
Contingent Claim Pricing with Applications to Financial Risk Management
Contingent Claim Pricing with Applications to Financial Risk Management By Hua Chen 2008 Committee Chair: Samuel H. Cox and Shaun Wang Major Academic Unit: Department of Risk Management and Insurance This is a multi-essay dissertation designed to explore the contingent claim pricing theory with non-tradable underlying assets, with emphasis on its applications to insurance and risk management. In the first essay, I apply the real option pricing theory and dynamic programming methods to address problems in the area of operational risk management. Particularly, I develop a two-stage model to help firms determine optimal switching triggers in the event of an influenza epidemic. In the second essay, I examine mortality securitization in an incomplete market framework. I build a jump-diffusion process into the original Lee-Carter model and explore alternative model with transitory versus permanent jump effects. I discuss pricing difficulties of the Swiss Re mortality bond (2003) and use the Wang transform to account for correlations of the mortality index over time. In the third essay, I study the valuation of the non-recourse provision in reverse mortgages. I model the various risks embedded in the HECM program and apply the conditional Esscher transform to price the non-recourse provision. I further examine the premium structure of HECM loans and investigate whether insurance premiums are adequate to cover expected claims
An Improvement in a Local Observer Design for Optimal State Feedback Control: The Case Study of HIV/AIDS Diffusion
The paper addresses the problem of an observer design for a nonlinear system for which a preliminary linear
state feedback is designed but the full state is not measurable. Since a linear control assures the fulfilment of
local approximated conditions, usually a linear observer is designed in these cases to estimate the state with
estimation error locally convergent to zero. The case in which the control contains an external reference, like
in regulations problems, is studied, showing that the solution obtained working with the linear approximation
to get local solutions produces non consistent results in terms of local regions of convergence for the system
and for the observer. A solution to this problem is provided, proposing a different choice for the observer
design which allows to obtain all conditions locally satisfied on the same local region in the neighbourhood of
a new equilibrium point. The case study of an epidemic spread control is used to show the effectiveness of the
procedure. The linear control with regulation term is present in this case because the problem is reconducted to
a Linear Quadratic Regulation problem. Simulation results show the differences between the two approaches
and the effectiveness of the proposed on
A linear quadratic regulator for nonlinear SIRC epidemic model
The control of an epidemic disease consists in introducing the strategies able to reduce the number of infected subjects by means of medication/quarantine actions, and the number of the subjects that could catch the disease through an informative campaign and, when available, a vaccination strategy. Some diseases, like the influenza, do not guarantee immunity; therefore, the subjects could get ill again by different strain of the same viral subtype. The epidemic model adopted in this paper introduces the cross-immune individuals; it is known in literature as SIRC model, since the classes of susceptible (S), infected (I), removed (R) and cross-immune (C) subjects are considered. Its control is herein determined in the framework of the linear quadratic regulator, by applying to the original nonlinear model the optimal control found on the linearized system. The results appear satisfactory, and the drawback of using a control law based on the linear approximation of the system is compensated by the advantages arising from such a solution: no costate equations to be solved and a solution depending on the current state evolution which allows a feedback implementation
Sequential Design for Ranking Response Surfaces
We propose and analyze sequential design methods for the problem of ranking
several response surfaces. Namely, given response surfaces over a
continuous input space , the aim is to efficiently find the index of
the minimal response across the entire . The response surfaces are not
known and have to be noisily sampled one-at-a-time. This setting is motivated
by stochastic control applications and requires joint experimental design both
in space and response-index dimensions. To generate sequential design
heuristics we investigate stepwise uncertainty reduction approaches, as well as
sampling based on posterior classification complexity. We also make connections
between our continuous-input formulation and the discrete framework of pure
regret in multi-armed bandits. To model the response surfaces we utilize
kriging surrogates. Several numerical examples using both synthetic data and an
epidemics control problem are provided to illustrate our approach and the
efficacy of respective adaptive designs.Comment: 26 pages, 7 figures (updated several sections and figures
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