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In this article, we address mechanism design for two-stage repeated stochastic games—a setting using which many emerging problems in electricity markets can be readily modeled. We introduce the notion of dominant strategy nonbankrupting equilibrium (DNBE) which requires players to make very few assumptions about the behaviors of other players in order to employ their equilibrium strategy. Consequently, a mechanism that renders truth-telling a DNBE could be quite effective in molding real-world behavior along truthful lines. We present a mechanism for two-stage repeated stochastic games that renders truth-telling a DNBE.

Dr. Le Xie is a Professor, Chancellor EDGES Fellow, and Presidential Impact Fellow in the Department of Electrical and Computer Engineering at Texas A&M, and the Assistant Director-Energy Digitization at Texas A&M Energy Institute. He was awarded the 2017 IEEE PES Outstanding Young Engineer Award for the best power engineer under 35. He is the founding chair of IEEE PES Subcommittee on Big Data & Analytics for Grid Operations.

The novel coronavirus disease (COVID-19) has rapidly spread around the globe in 2020, with the US becoming the epicenter of COVID-19 cases since late March. As the US begins to gradually resume economic activity, it is imperative for policymakers and power system operators to take a scientific approach to understanding and predicting the impact on the electricity sector. Here, we release a first-of-its-kind cross-domain open-access data hub, integrating data from across all existing US wholesale electricity markets with COVID-19 case, weather, mobile device location, and satellite imaging data. Leveraging cross-domain insights from public health and mobility data, we rigorously uncover a significant reduction in electricity consumption that is strongly correlated with the number of COVID-19 cases, degree of social distancing, and level of commercial activity.

This paper examines the dependence of network performance measures on network size and considers scaling results for large networks. We connect two performance measures that are well studied, but appear to be unrelated. The first measure is concerned with energy metrics, namely, the $\mathcal {H}_2$-norm of a network, which arises in control theory applications. The second measure is concerned with the notion of “tail risk,” which arises in economic and financial networks. We study the question of why such performance measures may deteriorate at a faster rate than the growth rate of the network. We first focus on the energy metric and its well-known connection to controllability Gramian of the underlying dynamical system. We show that undirected networks exhibit the most graceful energy growth rates as network size grows. This rate is quantified completely by the proximity of the spectral radius to unity or distance to instability. In contrast, we show that the simple characterization of energy in terms of network spectrum does not exist for directed networks. We demonstrate that for any fixed distance to instability, energy of a directed network can grow at an exponentially faster rate. We provide general methods for manipulating networks to reduce energy. In particular, we prove that certain operations that increase the symmetry in a network cannot increase energy (in an order sense). Additionally, we demonstrate that such operations can effectively reduce energy for many network topologies. Second, we focus on tail risk in economic and financial networks. In contrast to the $\mathcal {H}_2$-norm, which arises from computing the expectation of energy in the network, tail risk focuses on tail probability behavior of network variables. Although the two measures differ substantially, we show that they are precisely connected through the system Gramian. This surprising result explains why topology considerations rather than specific performance measures dictate the large-scale behavior of networks. Finally, we demonstrate the consistency of our theory with simulations on synthetic and real-life networks.

We investigate the use of variable speed limits for resilient operation of transportation networks, which are modeled as dynamical flow networks under local routing decisions. In such systems, some external inflow is injected to the so-called origin nodes of the network. The total inflow arriving at each node is routed to its operational outgoing links based on their current densities of traffic. The density on each link has first-order dynamics driven by the difference of its incoming and outgoing flows. A link fails if it reaches its jam density. Such failures may propagate in the network and cause a systemic failure. We show that larger link capacities, that is, the maximum flows that can be sustained by the links, are not always better for preventing systemic failures under local routing. Accordingly, we propose the use of variable speed limits to operate the links below their capacities, when necessary, to compensate for the lack of global information and coordination in routing decisions. We show that systemic failures under feasible external inflows can always be averted through proper selection of speed limits if the routing decisions are sufficiently responsive to local congestion and the network is initially uncongested. This is an attractive feature as it provides a practical alternative to building more physical capacity or altering routing decisions that are determined by social behavior.

In this paper, we deal with the stabilizability of a scalar plant through a noisy discrete channel. Our scheme can be regarded as a variation of the controllers based on dynamic quantizers introduced in [3] and [4], but our analysis based on Lyapunov function allows us to take into consideration more general discrete memoryless channels. Given a plant and a discrete memoryless channel we will provide, using control Lyapunov function ideas, a condition for the existence of an encoder/controller pair with a priori fixed memory that achieves stability. A construction procedure is also provided.

In this paper we consider the classical binary hypothesis testing problem where the iid samples are obtained through a channel. Our goal is to study the relationship between the channel capacity and the goodness of the estimation measured by the Chernoff information in order to get an upper bound on the estimation performances as well as some insight on the structure of the optimal channel.

In this paper, we address the stabilizability of uncertain systems in the presence of finite data-rate feedback. In our formulation, a finite data-rate link is used to transmit state measurements between the plant and the controller. We determine sufficient conditions for internal and external stabilizability of the feedback loop. Stability in the presence of uncertainty in the plant is analyzed using a small-gain argument. We show that larger uncertainty can be tolerated at the expense of higher transmission rates. A comparison is established between the sufficient conditions for robust stabilizability and the necessary conditions for the stability of the nominal model. We also suggest how our results can be used to determine the stabilizability of a class of non-linear systems.

We introduce a new method of model order selection: minimum description complexity (MDC). The approach is motivated by the Kullback-Leibler information distance. The method suggests to choose the model set for which the "model set relative entropy" is minimum. The proposed method is comparable with the existing order estimation methods such as AIC and MDL. We elaborate on the advantages of MDC over the available information theoretic approaches.

The problem of controlling the growth of thin compound-semiconductor films using Organometallic Vapor-Phase Epitaxy (OMVPE) is considered. This is a new application of control theory aimed at one of the key processes in the compound semiconductor manufacturing industry. As a first step, this research introduces the process to the controls community, presents a physics-based process model for III-V compounds, and discusses a systematic approach to controller design that accomodates nonlinearity and uncertainty in the system. The idea is that structure in the process model can be exploited through a change of coordinates to facilitate the use of linear design methodologies. Experimental results are then given demonstrating composition control of AlxGa1-xAs and thickness control of GaAs.

In this paper we study robust stability, in the lpsense, against structured perturbations of bounded lpnorm. The perturbations may be either linear time-varying, nonlinear time-varying, or nonlinear time-invariant. We develop exact tests for robust stability for each case in terms of convex optimization problems. These results are extended to solve the corresponding robust performance problems, with performance measured via the induced lpnorm.

The L1optimal control problem with additional constraints on the magnitude of the closed loop frequency response at fixed frequency points is considered. This problem is known to be equivalent to a convex optimization subject to infinite dimensional LMI. It is shown that the LMI problem can be approximated arbitrarily well by an infinite dimensional Linear Program. The main result of the paper states that, for multiblock problems, the computation of lower bounds to the optimal cost, based on approximating the dual linear programming problem by sequences of finite support, may fail to converge to the optimal cost of the infinite dimensional problem as the dimension of the approximation increases.

In this paper we consider the problem ofL1 sensitivity minimization for linear plants with commensurate input delays. We describe a procedure for computing the minimum performance, and we characterize optimal solutions. The computations involve solving a one-parameter family of finite-dimensional linear programs. Explicit solutions are presented for important special cases.

In this paper we characterize a class of indirect adaptive controllers that can stabilize a time invariant system subjected to both parametric and l∞to l∞bounded unstructured uncertainty. Pertaining to this class of controllers, a particular indirect adaptive scheme is proposed and an a prioricomputable upper bound on the size of the unstructured uncertainty, for which stability is ensured, is provided.

How can the details of who observes what affect the outcomes of economic, social, and political interactions? Our thesis is that outcomes do not depend merely on the status quo and the available (noisy) information on it; they also crucially depend on how the available pieces of information are allocated among strategic agents. We study the dependence of coordination outcomes on local information sharing. In the economic literature, common knowledge of the fundamentals leads to the standard case of multiple equilibria due to the self-fullling nature of agents' beliefs. The global-games framework has been used extensively as a toolkit for arriving at a unique equilibrium selection in the context of coordination games, which can model bank runs, currency attacks, and social uprisings, among others. Yet, there is a natural mechanism through which multiplicity can reemerge, while keeping information solely exogenous: the (exogenous) information structure per se, namely, the details of who observes what noisy observation. The aim of this paper is to understand the role of the exogenous information structure in the determination and characterization of equilibria in the coordination game. We answer the question of how the equilibria of the coordination game depend on the details of local information sharing. Our main contribution is to provide conditions for uniqueness and multiplicity that pertain solely to the details of information sharing. The findings in the present paper give an immediate answer as to the determinacy of equilibria using only the characterization of what agent observes what pieces of information. We build on the standard global game framework for coordination games with incomplete and asymmetric information and consider a coordination game in which each of a collection of agents decides whether to take a risky action (whose payoff depends on how many agents made the same decision, and the fundamentals) or a safe action, based on their noisy observations regarding the fundamentals. Generalizing away from the standard practice of considering only private and public signals, we allow for signals that are observed by arbitrary subsets of the agents. We refer to signals that are neither private nor public as local signals. We pose the following question: how do the equilibria of the coordination game depend on the information locality, i.e., on the details of local information sharing. Our key finding is that the number of equilibria is highly sensitive to the details of information locality. As a result, a new dimension of indeterminacy regarding the outcomes is being introduced: not only may the same fundamentals well lead to different outcomes in different societies, due to different realizations of the noisy observations; the novel message of this work is that the same realization of the noisy observations is compatible with different equilibrium outcomes in societies with different structures of local information sharing. In particular, we show that as long as a collection of agents share the same observations, and no other agent's observations overlap with their common observations, multiple equilibria arise. Identical observations is not, nevertheless, a necessary condition for multiplicity: we show that as long as the observations of a collection of agents form a cascade of containments, and no other agent's observations overlap with the observations of the collection, then multiplicity emerges. This is not to say however that common knowledge of information at the local level necessarily implies multiplicity: in particular, in the absence of identical observations or cascade of containments of observations, or if the condition of no overlap of information is violated, then, despite the presence of some signals that are common knowledge between agents, a unique equilibrium may be selected. In the case where each agent observes exactly one signal, we characterize the set of equilibria as a function of the details of the information structure. We show how the distance between the largest and smallest equilibria depends on how information is locally shared among the agents. In particular, the more equalized the sizes of the sets of agents who observe the same signal, the more diverse the information of each group becomes, heightening inter-group strategic uncertainty, and leading to a more refined set of equilibria. We use our characterization to study the set of equilibria in large coordination games. We show that as the number of agents grows, the game exhibits a unique equilibrium if and only if the largest set of agents with access to a common signal grows sublinearly in the number of agents, thus identifying a sharp threshold for uniqueness versus multiplicity.