Notes on the Solution of Dynamic Optimization Problems with Explicit Controls in Discrete-Time Economic Models

Йордан Йорданов, Андрей Василев - В работата се изследват методи за решаването на задачи на оптималното управление в дискретно време с безкраен хоризонт и явни управления. Дадена е обосновка на една процедура за решаване на такива задачи, базирана на множители на Лагранж, коята често се употребява в икономическата литература. Извеждени са необходимите условия за оптималност на базата на уравнения на Белман и са приведени достатъчни условия за оптималност при допускания, които често се използват в икономиката.

Characterization of Schrödinger Processes with Unbounded Potentials

2000 Mathematics Subject Classification: 49L20, 60J60, 93E20

Essays in environmental economic valuation and decision making in the presence of an environmental disaster

The first essay developed a respondent model of Bayesian updating for a double-bound dichotomous choice (DB-DC) contingent valuation methodology. I demonstrated by way of data simulations that current DB-DC identifications of true willingness-to-pay (WTP) may often fail given this respondent Bayesian updating context. Further simulations demonstrated that a simple extension of current DB-DC identifications derived explicitly from the Bayesian updating behavioral model can correct for much of the WTP bias. Additional results provided caution to viewing respondents as acting strategically toward the second bid. Finally, an empirical application confirmed the simulation outcomes. The second essay applied a hedonic property value model to a unique water quality (WQ) dataset for a year-round, urban, and coastal housing market in South Florida, and found evidence that various WQ measures affect waterfront housing prices in this setting. However, the results indicated that this relationship is not consistent across any of the six particular WQ variables used, and is furthermore dependent upon the specific descriptive statistic employed to represent the WQ measure in the empirical analysis. These results continue to underscore the need to better understand both the WQ measure and its statistical form homebuyers use in making their purchase decision. The third essay addressed a limitation to existing hurricane evacuation modeling aspects by developing a dynamic model of hurricane evacuation behavior. A household's evacuation decision was framed as an optimal stopping problem where every potential evacuation time period prior to the actual hurricane landfall, the household's optimal choice is to either evacuate, or to wait one more time period for a revised hurricane forecast. A hypothetical two-period model of evacuation and a realistic multi-period model of evacuation that incorporates actual forecast and evacuation cost data for my designated Gulf of Mexico region were developed for the dynamic analysis. Results from the multi-period model were calibrated with existing evacuation timing data from a number of hurricanes. Given the calibrated dynamic framework, a number of policy questions that plausibly affect the timing of household evacuations were analyzed, and a deeper understanding of existing empirical outcomes in regard to the timing of the evacuation decision was achieved.

Essays in Environmental Economic Valuation and Decision Making in the Presence of an Environmental Disaster

The first essay developed a respondent model of Bayesian updating for a double-bound dichotomous choice (DB-DC) contingent valuation methodology. I demonstrated by way of data simulations that current DB-DC identifications of true willingness-to-pay (WTP) may often fail given this respondent Bayesian updating context. Further simulations demonstrated that a simple extension of current DB-DC identifications derived explicitly from the Bayesian updating behavioral model can correct for much of the WTP bias. Additional results provided caution to viewing respondents as acting strategically toward the second bid. Finally, an empirical application confirmed the simulation outcomes. The second essay applied a hedonic property value model to a unique water quality (WQ) dataset for a year-round, urban, and coastal housing market in South Florida, and found evidence that various WQ measures affect waterfront housing prices in this setting. However, the results indicated that this relationship is not consistent across any of the six particular WQ variables used, and is furthermore dependent upon the specific descriptive statistic employed to represent the WQ measure in the empirical analysis. These results continue to underscore the need to better understand both the WQ measure and its statistical form homebuyers use in making their purchase decision. The third essay addressed a limitation to existing hurricane evacuation modeling aspects by developing a dynamic model of hurricane evacuation behavior. A household’s evacuation decision was framed as an optimal stopping problem where every potential evacuation time period prior to the actual hurricane landfall, the household’s optimal choice is to either evacuate, or to wait one more time period for a revised hurricane forecast. A hypothetical two-period model of evacuation and a realistic multi-period model of evacuation that incorporates actual forecast and evacuation cost data for my designated Gulf of Mexico region were developed for the dynamic analysis. Results from the multi-period model were calibrated with existing evacuation timing data from a number of hurricanes. Given the calibrated dynamic framework, a number of policy questions that plausibly affect the timing of household evacuations were analyzed, and a deeper understanding of existing empirical outcomes in regard to the timing of the evacuation decision was achieved.

Multiple robots formation manoeuvring and collision avoidance strategy

This paper presents a multiple robots formation manoeuvring and its collision avoidance strategy. The direction priority sequential selection algorithm is employed to achieve the raw path, and a new algorithm is then proposed to calculate the turning compliant waypoints supporting the multi-robot formation manoeuvre. The collision avoidance strategy based on the formation control is presented to translate the collision avoidance problem into the stability problem of the formation. The extension-decomposition-aggregation scheme is next applied to solve the formation control problem and subsequently achieve the collision avoidance during the formation manoeuvre. Simulation study finally shows that the collision avoidance problem can be conveniently solved if the stability of the constructed formation including unidentified objects can be satisfied.

Work Fluctuations in Bosonic Josephson Junctions

We calculate the first two moments and full probability distribution of the work performed on a system of bosonic particles in a two-mode Bose-Hubbard Hamiltonian when the self-interaction term is varied instantaneously or with a finite-time ramp. In the instantaneous case, we show how the irreversible work scales differently depending on whether the system is driven to the Josephson or Fock regime of the bosonic Josephson junction. In the finite-time case, we use optimal control techniques to substantially decrease the irreversible work to negligible values. Our analysis can be implemented in present-day experiments with ultracold atoms and we show how to relate the work statistics to that of the population imbalance of the two modes.

Decision making models embedded into a web-based tool for assessing pest infestation risk

Current practices in agricultural management involve the application of rules and techniques to ensure high quality and environmentally friendly production. Based on their experience, agricultural technicians and farmers make critical decisions affecting crop growth while considering several interwoven agricultural, technological, environmental, legal and economic factors. In this context, decision support systems and the knowledge models that support them, enable the incorporation of valuable experience into software systems providing support to agricultural technicians to make rapid and effective decisions for efficient crop growth. Pest control is an important issue in agricultural management due to crop yield reductions caused by pests and it involves expert knowledge. This paper presents a formalisation of the pest control problem and the workflow followed by agricultural technicians and farmers in integrated pest management, the crop production strategy that combines different practices for growing healthy crops whilst minimising pesticide use. A generic decision schema for estimating infestation risk of a given pest on a given crop is defined and it acts as a metamodel for the maintenance and extension of the knowledge embedded in a pest management decision support system which is also presented. This software tool has been implemented by integrating a rule-based tool into web-based architecture. Evaluation from validity and usability perspectives concluded that both agricultural technicians and farmers considered it a useful tool in pest control, particularly for training new technicians and inexperienced farmers.

MACVIA-ARIA Sentinel NetworK for allergic rhinitis (MASK-rhinitis): the new generation guideline implementation

Several unmet needs have been identified in allergic rhinitis: identification of the time of onset of the pollen season, optimal control of rhinitis and comorbidities, patient stratification, multidisciplinary team for integrated care pathways, innovation in clinical trials and, above all, patient empowerment. MASK-rhinitis (MACVIA-ARIA Sentinel NetworK for allergic rhinitis) is a simple system centred around the patient which was devised to fill many of these gaps using Information and Communications Technology (ICT) tools and a clinical decision support system (CDSS) based on the most widely used guideline in allergic rhinitis and its asthma comorbidity (ARIA 2015 revision). It is one of the implementation systems of Action Plan B3 of the European Innovation Partnership on Active and Healthy Ageing (EIP on AHA). Three tools are used for the electronic monitoring of allergic diseases: a cell phone-based daily visual analogue scale (VAS) assessment of disease control, CARAT (Control of Allergic Rhinitis and Asthma Test) and e-Allergy screening (premedical system of early diagnosis of allergy and asthma based on online tools). These tools are combined with a clinical decision support system (CDSS) and are available in many languages. An e-CRF and an e-learning tool complete MASK. MASK is flexible and other tools can be added. It appears to be an advanced, global and integrated ICT answer for many unmet needs in allergic diseases which will improve policies and standards.

Shortcuts to adiabaticity in the double well

123 p.

Effects of gestational and postnatal exposure to chronic intermittent hypoxia on diaphragm muscle contractile function in the rat

Alterations to the supply of oxygen during early life presents a profound stressor to physiological systems with aberrant remodeling that is often long-lasting. Chronic intermittent hypoxia (CIH) is a feature of apnea of prematurity, chronic lung disease, and sleep apnea. CIH affects respiratory control but there is a dearth of information concerning the effects of CIH on respiratory muscles, including the diaphragm—the major pump muscle of breathing. We investigated the effects of exposure to gestational CIH (gCIH) and postnatal CIH (pCIH) on diaphragm muscle function in male and female rats. CIH consisted of exposure in environmental chambers to 90 s of hypoxia reaching 5% O2 at nadir, once every 5 min, 8 h a day. Exposure to gCIH started within 24 h of identification of a copulation plug and continued until day 20 of gestation; animals were studied on postnatal day 22 or 42. For pCIH, pups were born in normoxia and within 24 h of delivery were exposed with dams to CIH for 3 weeks; animals were studied on postnatal day 22 or 42. Sham groups were exposed to normoxia in parallel. Following gas exposures, diaphragm muscle contractile, and endurance properties were examined ex vivo. Neither gCIH nor pCIH exposure had effects on diaphragm muscle force-generating capacity or endurance in either sex. Similarly, early life exposure to CIH did not affect muscle tolerance of severe hypoxic stress determined ex vivo. The findings contrast with our recent observation of upper airway dilator muscle weakness following exposure to pCIH. Thus, the present study suggests a relative resilience to hypoxic stress in diaphragm muscle. Co-ordinated activity of thoracic pump and upper airway dilator muscles is required for optimal control of upper airway caliber. A mismatch in the force-generating capacity of the complementary muscle groups could have adverse consequences for the control of airway patency and respiratory homeostasis.

Autonomous Pricing using Policy-Gradient Reinforcement Learning

Nella letteratura economica e di teoria dei giochi vi è un dibattito aperto sulla possibilità di emergenza di comportamenti anticompetitivi da parte di algoritmi di determinazione automatica dei prezzi di mercato. L'obiettivo di questa tesi è sviluppare un modello di reinforcement learning di tipo actor-critic con entropy regularization per impostare i prezzi in un gioco dinamico di competizione oligopolistica con prezzi continui. Il modello che propongo esibisce in modo coerente comportamenti cooperativi supportati da meccanismi di punizione che scoraggiano la deviazione dall'equilibrio raggiunto a convergenza. Il comportamento di questo modello durante l'apprendimento e a convergenza avvenuta aiuta inoltre a interpretare le azioni compiute da Q-learning tabellare e altri algoritmi di prezzo in condizioni simili. I risultati sono robusti alla variazione del numero di agenti in competizione e al tipo di deviazione dall'equilibrio ottenuto a convergenza, punendo anche deviazioni a prezzi più alti.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and operating constraints. The Optimal Power Flow problem is modeled as a large-scale mixed-discrete nonlinear programming problem. This paper proposes a method for handling the discrete variables of the Optimal Power Flow problem. A penalty function is presented. Due to the inclusion of the penalty function into the objective function, a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem. The obtained nonlinear programming problems are solved by a Primal-Dual Logarithmic-Barrier Method. Numerical tests using the IEEE 14, 30, 118 and 300-Bus test systems indicate that the method is efficient. (C) 2012 Elsevier B.V. All rights reserved.

An approach of optimal sensitivity applied in the tertiary loop of the automatic generation control

This paper proposes an approach of optimal sensitivity applied in the tertiary loop of the automatic generation control. The approach is based on the theorem of non-linear perturbation. From an optimal operation point obtained by an optimal power flow a new optimal operation point is directly determined after a perturbation, i.e., without the necessity of an iterative process. This new optimal operation point satisfies the constraints of the problem for small perturbation in the loads. The participation factors and the voltage set point of the automatic voltage regulators (AVR) of the generators are determined by the technique of optimal sensitivity, considering the effects of the active power losses minimization and the network constraints. The participation factors and voltage set point of the generators are supplied directly to a computational program of dynamic simulation of the automatic generation control, named by power sensitivity mode. Test results are presented to show the good performance of this approach. (C) 2008 Elsevier B.V. All rights reserved.

Optimal design of smart structures using bonded plezoelectrics for vibration control

Smart material technology has become an area of increasing interest for the development of lighter and stronger structures which are able to incorporate actuator and sensor capabilities for collocated control. In the design of actively controlled structures, the determination of the actuator locations and the controller gains, is a very important issue. For that purpose, smart material modelling, modal analysis methods, control and optimization techniques are the most important ingredients to be taken into account. The optimization problem to be solved in this context presents two interdependent aspects. The first one is related to the discrete optimal actuator location selection problem which is solved in this paper using genetic algorithms. The second is represented by a continuous variable optimization problem, through which the control gains are determined using classical techniques. A cantilever Euler-Bernoulli beam is used to illustrate the presented methodology.