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We focus on the problem of uncertainty informed allocation of medical resources (vaccines) to heterogeneous populations for managing epidemic spread. We tackle two related questions: (1) For a compartmental ordinary differential equation (ODE) model of epidemic spread, how can we estimate and integrate parameter uncertainty into resource allocation decisions? (2) How can we computationally handle both nonlinear ODE constraints and parameter uncertainties for a generic stochastic optimization problem for resource allocation? To the best of our knowledge current literature does not fully resolve these questions. Here, we develop a data-driven approach to represent parameter uncertainty accurately and tractably in a novel stochastic optimization problem formulation. We first generate a tractable scenario set by estimating the distribution on ODE model parameters using Bayesian inference with Gaussian processes. Next, we develop a parallelized solution algorithm that accounts for scenario-dependent nonlinear ODE constraints. Our scenario-set generation procedure and solution approach are flexible in that they can handle any compartmental epidemiological ODE model. Our computational experiments on two different non-linear ODE models (SEIR and SEPIHR) indicate that accounting for uncertainty in key epidemiological parameters can improve the efficacy of time-critical allocation decisions by 4-8%. This improvement can be attributed to data-driven and optimal (strategic) nature of vaccine allocations, especially in the early stages of the epidemic when the allocation strategy can crucially impact the long-term trajectory of the disease.

The world faces some of its greatest challenges of modern time and how we address them will have a dramatic impact on the life for generations to come. Simultaneously, control systems, consisting of information enriched by various degrees of analytics followed by decision-making, are pervading a variety of sectors, not only in engineering but beyond, into financial services, socio-economic analysis, entertainment and sports, and political and social sciences. Increased levels of automation are sought after in various sectors and being introduced into new domains. All of these advances and transformations urge a shift in the conversation toward how control systems can meet grand societal- scale challenges. The document seeks to chart a roadmap for the evolution of control systems, identifying several areas where our discipline can have an impact over the next decade.

In this paper, we study both multi-armed and contextual bandit problems in censored environments. Our goal is to estimate the performance loss due to censorship in the context of classical algorithms designed for uncensored environments. Our main contributions include the introduction of a broad class of censorship models and their analysis in terms of the effective dimension of the problem -- a natural measure of its underlying statistical complexity and main driver of the regret bound. In particular, the effective dimension allows us to maintain the structure of the original problem at first order, while embedding it in a bigger space, and thus naturally leads to results analogous to uncensored settings. Our analysis involves a continuous generalization of the Elliptical Potential Inequality, which we believe is of independent interest. We also discover an interesting property of decision-making under censorship: a transient phase during which initial misspecification of censorship is self-corrected at an extra cost, followed by a stationary phase that reflects the inherent slowdown of learning governed by the effective dimension. Our results are useful for applications of sequential decision-making models where the feedback received depends on strategic uncertainty (e.g., agents' willingness to follow a recommendation) and/or random uncertainty (e.g., loss or delay in arrival of information)., 45 pages, 5 figures, NeurIPS 2022

The transition to a deeply decarbonized energy system requires coordinated planning of infrastructure investments and operations serving multiple end-uses while considering technology and policy-enabled interactions across sectors. Electricity and natural gas (NG), which are vital vectors of today's energy system, are likely to be coupled in different ways in the future, resulting from increasing electrification, adoption of variable renewable energy (VRE) generation in the power sector and policy factors such as cross-sectoral emissions trading. This paper develops a least-cost investment and operations model for joint planning of electricity and NG infrastructures that considers a wide range of available and emerging technology options across the two vectors, including carbon capture and storage (CCS) equipped power generation, low-carbon drop-in fuels (LCDF) as well as long-duration energy storage (LDES). The model incorporates the main operational constraints of both systems and allows each system to operate under different temporal resolutions consistent with their typical scheduling timescales. We apply the modeling framework to evaluate power-NG system outcomes for the U.S. New England region under different technology, decarbonization goals, and demand scenarios. Under a global emissions constraint, ranging between 80-95\% emissions reduction compared to 1990 levels, the least-cost solution disproportionately relies on using the available emissions budget to serve non-power NG demand and results in the power sector using only 15-43\% of the emissions budget.

This paper presents a modeling approach for probabilistic estimation of hurricane wind-induced damage to infrastructural assets. In our approach, we employ a Nonhomogeneous Poisson Process (NHPP) model for estimating spatially-varying probability distributions of damage as a function of hurricane wind field velocities. Specifically, we consider a physically-based, quadratic NHPP model for failures of overhead assets in electricity distribution systems. The wind field velocities are provided by Forecasts of Hurricanes using Large-Ensemble Outputs (FHLO), a framework for generating probabilistic hurricane forecasts. We use FHLO in conjunction with the NHPP model, such that the hurricane forecast uncertainties represented by FHLO are accounted for in estimating the probability distributions of damage. Furthermore, we evaluate the spatial variability and extent of hurricane damage under key wind field parameters (intensity, size, and asymmetries). By applying our approach to prediction of power outages (loss-of-service) in northwestern Florida due to Hurricane Michael (2018), we demonstrate a statistically significant relationship between outage rate and failure rate. Finally, we formulate parametric models that relate total damage and financial losses to the hurricane parameters of intensity and size. Overall, this paper's findings suggest that our approach is well-suited to jointly account for spatial variability and forecast uncertainty in the damage estimates, and is readily applicable to prediction of system loss-of-service due to the damage., Submitted to Risk Analysis, 21 pages (main text), 17 figures, includes appendix

In this paper, we address the existence and computation of competitive equilibrium in the transportation market for autonomous carpooling first proposed by [Ostrovsky and Schwarz, 2019]. At equilibrium, the market organizes carpooled trips over a transportation network in a socially optimal manner and sets the corresponding payments for individual riders and toll prices on edges. The market outcome ensures individual rationality, stability of carpooled trips, budget balance, and market clearing properties under heterogeneous rider preferences. We show that the question of market's existence can be resolved by proving the existence of an integer optimal solution of a linear programming problem. We characterize conditions on the network topology and riders' disutility for carpooling under which a market equilibrium can be computed in polynomial time. This characterization relies on ideas from the theory of combinatorial auctions and minimum cost network flow problem. Finally, we characterize a market equilibrium that achieves strategyproofness and maximizes welfare of individual riders.

The instrumentation of infrastructure systems by embedded sensors, computation, and communication networks has enabled significant advances in their management. Examples include monitoring of structural health, traffic congestion, environmental hazards, and energy usage. The use of homogeneous (especially, commercially available off-the-shelf) information technology (IT) solutions makes infrastructure systems subject to correlated hardware malfunctions and software bugs. Over the past decade, many concerns have been raised about the vulnerabilities of infrastructure systems to both random failures and security attacks. Cyber-security of Supervisory Control and Data Acquisition (SCADA) systems is especially important, because these systems are employed for sensing and control of large physical infrastructures. So far, the existing research in robust and fault-tolerant control does not account for cyber attacks on networked control system (NCS) components. Also, the existing research in computer security neither considers the attacks targeting NCS components nor accounts for their interactions with the physical system. The goal of this thesis is to bridge this gap by focusing on (1) security threat assessment, (2) model-based attack diagnosis, and (3) resilient control design. First, cyber-security assessment for SCADA systems is performed based on well-defined attacker and defender objectives. The mathematical model of SCADA systems considered in this work has two control levels: regulatory control using distributed proportional-integral (PI) controllers, and supervisory fault diagnosis based on approximate dynamical system models. The performance of a PI control based regulatory scheme and a model-based supervisory diagnostic scheme is studied under a class of deception attacks. In order to test the system resilience, a class of stealthy attacks which can evade detection by SCADA systems is presented. Second, design of attack diagnosis schemes that incorporate the knowledge of physical dynamics of the system is presented. For SCADA systems used to manage water canal networks, an observer-based attack diagnostic scheme, in which each observer estimates the state of a reduced-order flow model, is presented. The observer parameters are computed using a convex optimization method, and the performance of this scheme is tested on a number of attack scenarios. An application of the theoretical results is illustrated by a field operational test performed on the SCADA system of the Gignac water canal system, located in Montpellier, France. A successful experimental cyber-attack on the sensors and actuators of this canal network revealed new vulnerabilities of the current SCADA system implementation. Another illustration includes security analysis of two benchmark scenarios: the Tennessee Eastman process control system (TE-PCS) and a power system state estimator (PSSE). In both these cases, model-based statistical detection schemes are used to study stealthy deception attacks. For the case of TE-PCS, design of practically implementable attack-detection and response mechanisms to maintain operational safety is presented. For the case of PSSE, it is assumed that the attacker only has a partial knowledge of the actual system model. For a set of attacker objectives, the trade-off between the attacker knowledge and possible impact of a successful attack on the performance of false data detection schemes is studied. Third, the stability of linear hyperbolic systems of PDEs when the boundary control actions and the system parameters switch discontinuously between a finite set of modes is studied. Switched PDE models can describe a class of fault and attack scenarios resulting from intermittent withdrawals through offtake nodes and compromise of sensor-control data. Motivated by such scenarios, a new condition for stability of linear hyperbolic systems of PDEs under arbitrary switching of boundary control actions and system parameters is derived. A class of switching attack strategies is presented, which violate the stability condition and result in unstable flow dynamics.Fourth, the problem of controlling stochastic linear systems for networked control settings is considered when the sensor-control data is prone to packet loss and jamming. For a class of packet drop models, feedback control policies which minimize a given objective function subject to safety constraints are synthesized. For marginally stable systems, under mild hypotheses on the noise introduced by the control channel and large enough control authority, the synthesis of a control policy that render the state of the closed-loop system mean-square bounded is presented.Finally, a class of games involving discrete interdependent risks is considered when each player is a NCS, and their security is interdependent due to the exposure to network induced risks. The problem of security decisions of individual players is formulated as a two-stage non-cooperative game defined as follows: in the first stage, the players decide whether to invest in security or not; and in the second stage, they apply control inputs to minimize the average operational costs. The characterization of the equilibria of the game is presented, which includes the determination of the individually optimal security levels. The presence of interdependent security causes a negative externality, and the individual players tend to under invest in security relative to the social optimum. From these results, for a wide parameter range, public policy incentivising higher security investments is desirable.

The tandem fluid queueing model is a useful tool for performance analysis and control design for a variety of transportation systems. In this article, we study the joint impact of stochastic capacity and spillback on the long-time properties of this model. Our analysis focuses on the system of two fluid queueing links in series. The upstream link has a constant capacity (saturation rate) and an infinite buffer size. The downstream link has a stochastic capacity and a finite buffer size. Queue spillback occurs when the the downstream link is full. We derive a necessary condition and a sufficient condition for the total queue length to be bounded on average. The necessary (resp. sufficient) condition leads to an upper (resp. lower) bound for the throughput of the two-link system. Using our results, we analyze the sensitivity of throughput of the two-link system with respect to the frequency and intensity of capacity disruptions, and to the buffer size. In addition, we discuss how our analysis can be extended to feedback-controlled systems and to networks consisting of merges and splits.

In this paper, we study the problem of traffic management in highways facing stochastic perturbations. To model the macroscopic traffic flow under perturbations, we use cell-transmission model with Markovian capacities. The decision variables are: (i) the admissible flow through each on-ramp, and (ii) whether individual on-ramps are metered to prioritize the mainline traffic or not. The objective is to maximize the throughput while ensuring that on-ramp queues remain bounded on average. We develop a computational approach to solving this stability-constrained, throughput-maximization problem. We establish a mixed-integer linear program for throughput maximization and construct an algorithm that gives the optimal solution in particular settings. We illustrate the performance benefits of the proposed approach through a computational study on a segment of Interstate 210 in California, USA., 27 pages

In this paper, we develop a novel mechanism for reducing volatility of residential demand for electricity. We construct a reward-based (rebate) mechanism that provides consumers with incentives to shift their demand to off-peak time. In contrast to most other mechanisms proposed in the literature, the key feature of our mechanism is its modest requirements on user preferences, i.e., it does not require exact knowledge of user responsiveness to rewards for shifting their demand from the peak to the off-peak time. Specifically, our mechanism utilizes a probabilistic reward structure for users who shift their demand to the off-peak time, and is robust to incomplete information about user demand and/or risk preferences. We approach the problem from the public good perspective, and demonstrate that the mechanism can be implemented via lottery-like schemes. Our mechanism permits to reduce the distribution losses, and thus improve efficiency of electricity distribution. Finally, the mechanism can be readily incorporated into the emerging demand response schemes (e.g., the time-of-day pricing, and critical peak pricing schemes), and has security and privacy-preserving properties., National Science Foundation (U.S.) (Grant CNS-1239166), National Science Foundation (U.S.) (Grant CNS-0910711), National Science Foundation (U.S.) (CCF-0424422)

This article studies the value of information in route choice decisions when a fraction of players have access to high accuracy information about traffic incidents relative to others. To model such environments, we introduce a Bayesian congestion game, in which players have private information about incidents, and each player chooses her route on a network of parallel links. The links are prone to incidents that occur with an ex-ante known probability. The demand is comprised of two player populations: one with access to high accuracy incident information and another with low accuracy information, i.e. the populations differ only by their access to information. The common knowledge includes: (i) the demand and route cost functions, (ii) the fraction of highly-informed players, (iii) the incident probability, and (iv) the marginal type distributions induced by the information structure of the game. We present a full characterization of the Bayesian Wardrop Equilibrium of this game under the assumption that low information players receive no additional information beyond common knowledge. We also compute the cost to individual players and the social cost as a function of the fraction of highly-informed players when they receive perfectly accurate information. Our first result suggests that below a certain threshold of highly-informed players, both populations experience a reduction in individual cost, with the highly-informed players receiving a greater reduction. However, above this threshold, both populations realize the same equilibrium cost. Secondly, there exists another (lower or equal) threshold above which a further increase in the fraction of highly-informed players does not reduce the expected social costs. Thus, once a sufficiently large number of players are highly informed, wider distribution of more accurate information is ineffective at best, and otherwise socially harmful.

The smart grid refers to the modernization of the power grid infrastructure with new technologies, enabling a more intelligently networked automated system with the goal of improving efficiency, reliability, and security, while providing more transparency and choices to electricity customers. A key technology being widely deployed on the consumption side of the grid is advanced metering infrastructure (AMI)., National Science Foundation (U.S.) (Award CNS-1239054)

We propose a raffle-based scheme for the decongestion of a shared resource. Our scheme builds on ideas from the economic literature on incentivizing contributions to a public good. We formulate a game-theoretic model for the decongestion problem in a setup with a finite number of users, as well as in a setup with an infinite number of non-atomic users. We analyze both setups, and show that the former converges toward the latter when the number of users becomes large. We compare our results to existing results for the public good provision problem. Overall, our results establish that raffle-based schemes are useful in addressing congestion problems., National Science Foundation (U.S.) (Grant CNS-0910711), National Science Foundation (U.S.) (Grant CCF-0424422), United States. Air Force Office of Scientific Research (FA9550-06-1-0244)

International audience

Infrastructure inspection and maintenance decision making is a stochastic and partially observable problem. This thesis presents a learning and decision-making approach for developing optimal joint inspection and maintenance policies for civil infrastructure facilities under performance model uncertainty and partially observable condition state. Joint inspection and maintenance decision making refers to the cost-effective policies that capture the interactions between the inspections, and the maintenance and rehabilitation decisions. Performance model uncertainty is the uncertainty about the actual facility deterioration model. Partially observation condition states imply that the true or latent condition of the facility is not captured by the measurement technology used for inspecting the facility due to measurement errors. The proposed approach models single facility inspection and maintenance decision-making problem as a partially observable Markov decision process. The data collected during the agency-facility interaction is used to learn the maximum likelihood estimate of performance model using the Baum-Welch algorithm. Both offline and online versions of the learning algorithm are presented. The probing-optimizing dichotomy, also known as exploration-exploitation dilemma, in choosing between the best strategy based on the past knowledge of deterioration and the strategy that provides information leading to better performance model is also illustrated. Once a set of performance models is learned, each of the models is quantitatively compared with the corresponding true model using an information theoretic measure known as asymmetric Kullback-Leibler divergence to determine its goodness. It is also shown that given a set of new observation sequences gathered after the model learning, each of the sequences or the entire set of sequences can be assigned the model that gives the least log-likelihood on that sequence or the set. This can help in classifying the facility deterioration into different deterioration modes like slow, medium, or fast. Finally, an exact algorithm for arriving at optimal inspection and maintenance decision-making policies is described. It is argued that the proposed approach scores over other recently developed adaptive control approaches in that it directly learns the best model from historical data instead of maintaining and updating beliefs over a set of pre-selected models. Furthermore, since the proposed learning approach is model-based, it makes more efficient use of costly data as compared to the model-less learning approaches. Keywords: Infrastructure Inspection and Maintenance, Baum-Welch Algorithm, Kullback-Liebler Divergence, Sequence Classification, Partially Observable Markov Decision Process, Reinforcement Learning.