Search

In addition to its public health crisis, COVID-19 pandemic has led to the shutdown and closure of workplaces with an estimated total cost of more than ${\$}$ 16 trillion. Given the long hours an average person spends in buildings and indoor environments, this research article proposes data-driven control strategies to design optimal indoor airflow to minimize the exposure of occupants to viral pathogens in built environments. A general control framework is put forward for designing an optimal velocity field and proximal policy optimization, a reinforcement learning algorithm is employed to solve the control problem in a data-driven fashion. The same framework is used for optimal placement of disinfectants to neutralize the viral pathogens as an alternative to the airflow design when the latter is practically infeasible or hard to implement. We show, via computational simulations, that the control agent learns the optimal policy in both scenarios within a reasonable time. The proposed data-driven control framework in this study will have significant societal and economic benefits by setting the foundation for an improved methodology in designing case-specific infection control guidelines that can be realized by affordable ventilation devices and disinfectants. Note to Practitioners—This paper is motivated by the problem of COVID-19 infection spread in enclosed spaces but it also applies to other airborne pathogens. Airborne disease contagion often takes place in indoor environments; however, ventilation systems are almost never designed to take this into account so as to contain the spread of the pathogens. This is mainly because airflow design requires solving high-dimensional nonlinear partial differential equations known as Navier Stokes equations in fluid dynamics. In this paper, we propose a data-driven approach for solving the control problem of pathogen containment without solving the fluid dynamics equations. To this end, we first mathematically formulate the problem as an optimal control problem and then cast it as a reinforcement learning (RL) task. Reinforcement learning is the data-driven science of sequential decision-making and control in which the controller finds an optimal solution by systematic trial and error and without access to the system dynamics, i.e. fluid and pathogen dynamics in this paper. We employ an state-of-the-art RL algorithm, called PPO, to solve for optimal airflow in a room so as to minimize the exposure risk of occupants. Once it is calculated, the optimal airflow could be realized, via reverse engineering, by proper placement of the ventilation equipment, e.g. inlets, outlets, and fans. As an alternative to the airflow design, we use the same proposed data-driven techniques to find an optimal placement for pathogen disinfectants if there exists one, such as, hydrogen peroxide for COVID-19. Our results show the efficacy of our data-driven approach in designing an steady-state controller with full access to the system states. In future research, we will address the controller design with sparse measurements of the system states.

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.

We study the role of local information channels in enabling coordination among strategic agents. Building on the standard finite-player global games framework, we show that the set of equilibria of a coordination game is highly sensitive to how information is locally shared among different agents. In particular, we show that the coordination game has multiple equilibria if there exists a collection of agents such that (i) they do not share a common signal with any agent outside of that collection and (ii) their information sets form an increasing sequence of nested sets. Our results thus extend the results on the uniqueness and multiplicity of equilibria beyond the well-known cases in which agents have access to purely private or public signals. We then provide a characterization of the set of equilibria as a function of the penetration of local information channels. We show that the set of equilibria shrinks as information becomes more decentralized. Keywords: coordination; local information; social networks; global games. Subject classifications: games/group decisions: economics; network/graphs. Area of review: Special Issue on Information and Decisions in Social and Economic Networks. History: Received July 2013; revisions received October 2014, January 2015; accepted February 2015. Published online in Articles in Advance November 12, 2015., 1. Introduction Coordination problems lie at the heart of many economic and social phenomena such as bank runs, social uprisings, and the adoption of new standards or technologies. The common [...]

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.

We characterize the role played by memory when linear time-invariant systems interact. This study is of interest as the phenomenon that occurs in this setting is arguably the same phenomenon that governs some cascading failure and contagion effects in interconnected systems. We aim to later extend solutions presented in this paper to problems in other desired settings. The characterization relies on basic methods in homological algebra, and is reminiscent of the rank-nullity theorem of linear algebra. Interconnection of systems is first expressed as an exact sequence, then loss of memory causes a loss of exactness, and finally exactness is recovered through specific algebraic invariants of the systems that encode the role of memory. We thus introduce a new invariant, termed lag, of linear time-invariant systems and characterize the role of memory in terms of the lag. We discuss properties of the lag, and prove several results regarding the characterization. [ABSTRACT FROM AUTHOR]

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.

Robustness of distributed routing policies is studied for dynamical networks, with respect to adversarial disturbances that reduce the link flow capacities. A dynamical network is modeled as a system of ordinary differential equations derived from mass conservation laws on a directed acyclic graph with a single origin-destination pair and a constant total outflow at the origin. Routing policies regulate the way the total outflow at each nondestination node gets split among its outgoing links as a function of the current particle density, while the outflow of a link is modeled to depend on the current particle density on that link through a flow function. The dynamical network is called partially transferring if the total inflow at the destination node is asymptotically bounded away from zero, and its weak resilience is measured as the minimum sum of the link-wise magnitude of disturbances that make it not partially transferring. The weak resilience of a dynamical network with arbitrary routing policy is shown to be upper bounded by the network's min-cut capacity and, hence, is independent of the initial flow conditions. Moreover, a class of distributed routing policies that rely exclusively on local information on the particle densities, and are locally responsive to that, is shown to yield such maximal weak resilience. These results imply that locality constraints on the information available to the routing policies do not cause loss of weak resilience. Fundamental properties of dynamical networks driven by locally responsive distributed routing policies are analyzed in detail, including global convergence to a unique limit flow. The derivation of these properties exploits the cooperative nature of these dynamical systems, together with an additional stability property implied by the assumption of monotonicity of the flow as a function of the density on each link. [ABSTRACT FROM AUTHOR]

Strong resilience properties of dynamical networks are analyzed for distributed routing policies. The latter are characterized by the property that the way the outflow at a non-destination node gets split among its outgoing links is allowed to depend only on local information about the current particle densities on the outgoing links. The strong resilience of the network is defined as the infimum sum of link-wise flow capacity reductions making the asymptotic total inflow to the destination node strictly less than the total outflow at the origin. A class of distributed routing policies that are responsive to local information is shown to yield the maximum possible strong resilience under such local information constraints for an acyclic dynamical network with a single origin-destination pair. The maximal achievable strong resilience is shown to be equal to the minimum node residual capacity of the network. The latter depends on the limit flow of the unperturbed network and is defined as the minimum, among all the non-destination nodes, of the sum, over all the links outgoing from the node, of the differences between the maximum flow capacity and the limit flow of the unperturbed network. We propose a simple convex optimization problem to solve for equilibrium flows of the unperturbed network that minimize average delay subject to strong resilience guarantees, and discuss the use of tolls to induce such an equilibrium flow in traffic networks. Finally, we present illustrative simulations to discuss the connection between cascaded failures and the resilience properties of the network. [ABSTRACT FROM AUTHOR]

Consider an agent who seeks to traverse the shortest path in a graph having random edge weights. If the agent has no side information about the realizations of the edge weights, it should simply take the path of least average length. We consider a generalization of this framework whereby the agent has access to a limited amount of side information about the edge weights ahead of choosing a path. We define a measure for information quantity, provide bounds on the agent's performance relative to the amount of side information it receives, and present algorithms for optimizing side information. The results are based on a new graph characterization tied to shortest path optimization. [ABSTRACT FROM AUTHOR]

A set of N independent Gaussian linear time-invariant systems is observed by M sensors whose task is to provide a steady-state causal estimate minimizing the mean-square error on the system states, subject to additional measurement costs. The sensors can switch between systems instantaneously, and there are additional resource constraints, for example on the number of sensors that can observe a given system simultaneously. We first derive a tractable relaxation of the problem, which provides a bound on the achievable performance. This bound can be computed by solving a convex program involving linear matrix inequalities, and moreover this program can be decomposed into coupled smaller dimensional problems. In the scalar case with identical sensors, we give an analytical expression of an index policy proposed in a more general context by Whittle. In the general case, we develop open-loop periodic switching policies whose performance matches the bound arbitrarily closely. [ABSTRACT FROM AUTHOR]

In this note, we demonstrate the use of a control oriented notion of finite state input/output approximation to synthesize correct-by-design controllers for hybrid plants under sensor limitations. Specifically, we consider the problem of designing stabilizing switching controllers for a pair of unstable homogeneous second order systems with binary output feedback. In addition to yielding a deterministic finite state approximate model of the hybrid plant, our approach allows one to efficiently establish a useable upper bound on the quality of approximation, and leads to a discrete optimization problem whose solution immediately provides a certified finite state controller for the plant. The resulting controller consists of a deterministic finite state observer and a corresponding full state feedback control law. [ABSTRACT FROM AUTHOR]

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.

Our previous work has been devoted to designing asymptotically stabilizing switching controllers for a class of second order LTI plants. Here, we extend the results of our previous work by proving that, when a plant can be asymptotically stabilized using a particular switching architecture, the overall closed-loop interconnection is also finite L2 gain stable. We shall first prove this result for a simplified problem in which a portion of the switching architecture has full access to the state of the plant and shall then extend to the case where the architecture only has access to the plant output by designing an appropriate observer. [ABSTRACT FROM AUTHOR]

In this note, we prove that dynamic programming value iteration converges uniformly for discrete-time homogeneous systems and continuous-time switched homogeneous systems. For discrete-time homogeneous systems, rather than discounting the cost function (which exponentially decreases the weights of the cost of future actions), we show that such systems satisfy approximate dynamic programming conditions recently developed by Rantzer, which provides a uniform bound on the convergence rate of value iteration over a compact set. For continuous-time switched homogeneous system, we present a transformation that generates an equivalent discrete-time homogeneous system with an additional "sampling" input for which discrete-time value iteration is compatible, and we further show that the inclusion of homogeneous switching costs results in a continuous value function. [ABSTRACT FROM AUTHOR]

This paper develops a generalization of the balanced truncation algorithm applicable to a class of discrete-time stochastic jump linear systems. The approximation error, which is captured by means of the stochastic L2 gain, is bounded from above by twice the sum of singular numbers associated to the truncated states, similar to the case of linear time-invariant systems. A two step model reduction algorithm for hidden Markov models is also developed. The first step relies on the aforementioned balanced truncation algorithm due to a topological equivalence established between hidden Markov models and a subclass of stochastic jump linear systems. In a second step the positivity constraints, which reflect the hidden Markov model structure, are enforced by solving a low dimensional optimization problem. [ABSTRACT FROM AUTHOR]

This paper addresses fundamental limitations of feedback using information theoretic conservation laws and flux arguments. The paper has two parts. In the first part, we derive a conservation law dictating that causal feedback cannot reduce the differential entropy inserted in the loop by external sources. An interpretation of this result is that the total randomness induced by disturbances, as measured by differential entropy, cannot be reduced by causal feedback; it can only be re-allocated in time or in frequency (if well defined). Under asymptotic stationarity assumptions, this result has a spectral representation which constitutes an extension of Bode's inequality for arbitrary feedback. Our proofs make clear the role of causality, as well as how stability assumptions impact the final result. In the second part, we derive an inequality unveiling that the feedback loop must be able to convey information originating from two independent sources: 1) initial states of the physical plant; 2) exogenous disturbance signals. By using such principle, we construct a variety of information rate (information flux) inequalities. Furthermore, we derive a universal performance bound which is parameterized solely by the feedback capacity and the parameters of the plant. The latter is a new fundamental limitation, which is different from Bode's classical result, indicating that finite feedback capacity brings a new type of performance bound. [ABSTRACT FROM AUTHOR]

Abstract-This paper considers a network in which a set of vehicles is responsible for picking up and delivering messages that arrive according to a Poisson process. Message pickup and delivery locations are uniformly distributed in a convex region. The vehicles are required to pickup and deliver the messages so that the average delay is minimized. It is required that the vehicle that picks up a message must be the one to deliver it. This problem is called the dynamic pickup and delivery problem (DPDP) and has applications in the context of autonomous vehicles and wireless ad hoc networks. The control policies considered are separable into two parts: an assignment policy used by a centralized controller to assign arriving messages to the vehicles for service and a service policy used by each vehicle to determine the service routes through its assigned messages. Lower bounds are provided on the delay achievable by separable control policies that depend on the information constraints in place. It is proved that the optimal average delay scaling can be reduced when message destination information is available to the centralized controller in addition to the message source information. The paper also provides policies that achieve these scaling bounds, proving that these bounds are tight. [ABSTRACT FROM AUTHOR]

In this paper, we analyze and derive conditions for stability of a feedback system in which the plant and feedback controller are separated by a noiseless finite-rate communication channel. We allow for two deterministic classes of reference inputs to excite the system, and derive sufficient conditions for input-output (IO) stability as a function of the encoding strategy and controller. We first construct an encoder as a quantizer that can have infinite memory and can be time-varying, in that the strategy it follows to allocate a total of R bits to its inputs, is a function of time. This construction of the quantizer leads to the result that the set of allocation strategies that maintains stability for each class of reference signals is convex, allowing the search for the most efficient strategy to ensure stability to be formulated as a convex optimization problem. We then synthesize quantizers and time-varying controllers to minimize the rate required for stability and to track commands. Examples presented in this paper demonstrate how this framework enables computationally efficient methods for simultaneously designing quantizers and controllers for given plants. Furthermore, we observe that our finite memory quantizers that minimize the rate required for stability do not reduce to trivial memoryless bit-allocation strategies. [ABSTRACT FROM AUTHOR]

Systems over finite alphabets are discrete-time systems whose input and output signals take their values in finite sets. Three notions of input/output stability (gain stability, incremental stability and external stability) that are particularly applicable to this class of systems are proposed and motivated through examples. New formulations for generalized small gain and incremental small gain theorems are presented, thus showing that gain stability and incremental stability are useful robustness measures. The paper then focuses on deterministic finite state machine (DFM) models. For this class, the problems of verifying gain stability, incremental stability, and corresponding gain bounds are shown to reduce to searching for an appropriate storage function. These problems are also shown to be related to the problem of verifying the nonexistence of negative cost cycles in an appropriately constructed network. Using this insight and based on a solution approach for discrete shortest path problems, a strongly polynomial algorithm is proposed. Finally, incremental stability and external stability are shown to be equivalent notions for this class of systems. [ABSTRACT FROM AUTHOR]

In this note, we consider a set up in which the plant and controller are local to each other, but are together driven by a remote reference signal that is transmitted through a noisy discrete channel. Our goal is to design codeword lengths of block source and channel encoders, and a controller to meet a model matching performance objective. Such design problems are difficult in general, as there is a strong interplay between control objectives and communication constraints, which forces the synthesis of controllers and encoder-decoder pairs to be done simultaneously. Current approaches typically fix one, while the other is designed to meet some objective. We first construct a model matching performance metric that captures the tradeoffs between coding the reference command to achieve more accuracy at the remote site and designing a controller to meet performance. We then simultaneously synthesize the controller and encoder codeword lengths that meet the specified objective for a first-order plant and model case. Finally, we illustrate performance sensitivity to the poles of the plant and model, and to the channel noise. [ABSTRACT FROM AUTHOR]

In this paper, we study fundamental limitations of disturbance attenuation of feedback systems, under the assumption that the controller has a finite horizon preview of the disturbance. In contrast with prior work, we extend Bode's integral equation for the case where the preview is made available to the controller via a general, finite capacity, communication system. Under asymptotic stationarity assumptions, our results show that the new fundamental limitation differs from Bode's only by a constant, which quantifies the information rate through the communication system. In the absence of asymptotic stationarity, we derive a universal lower bound which uses Shannon's entropy rate as a measure of performance. By means of a case-study, we show that our main bounds may be achieved. [ABSTRACT FROM AUTHOR]

We study the stabilizability of uncertain stochastic systems in the presence of finite capacity feedback. Motivated by the structure of communication networks, we consider a variable rate digital link. Such link is used to transmit state measurements between the plant and the controller. We derive necessary and sufficient conditions for internal and external stabilizability of the feedback loop. In accordance with previous publications, stabilizability of unstable plants is possible if and only if the link's average transmission rate is above a positive critical value. In addition, stability in the presence of uncertainty in the plant is analyzed using a small-gain argument. We also show that robustness can be increased at the expense of a higher transmission rate. [ABSTRACT FROM AUTHOR]

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.

This paper presents an entirely new constructive global analysis methodology for a class of hybrid systems known as piecewise linear systems (PLS). This methodology infers global properties of PLS solely by studying the behavior at switching surfaces associated with PLS. The main idea is to analyze impact maps, i.e., maps from one switching surface to the next switching surface. Such maps are known to be "unfriendly" maps in the sense that they are highly nonlinear, multivalued, and not continuous. We found, however, that an impact map induced by an linear time-invariant flow between two switching surfaces can be represented as a linear transformation analytically parametrized by a scalar function of the state. This representation of impact maps allows the search for surface Lyapunov functions (SuLF) to be done by simply solving a semidefinite program, allowing global asymptotic stability, robustness, and performance of limit cycles and equilibrium points of PLS to be efficiently checked. This new analysis methodology has been applied to relay feedback, on/off and saturation systems, where it has shown to be very successful in globally analyzing a large number of examples. In fact, it is still an open problem whether there exists an example with a globally stable limit cycle or equilibrium point that cannot be successfully analyzed with this new methodology. Examples analyzed include systems of relative degree larger than one and of high dimension, for which no other analysis methodology could be applied. This success in globally analyzing certain classes of PLS has shown the power of this new methodology, and suggests its potential toward the analysis of larger and more complex PLS. [ABSTRACT FROM AUTHOR]

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.

Assesses the distributed control of spatially invariant systems. Emphasis on spatial convolutions; Description of control design problem; Structure of quadratically optimal controllers.

Studies the global stability of relay feedback systems. Introduction of a novel constructive global analysis methodology for piecewise linear systems; Decomposition and stability of Poincare maps; Representation of Poincare maps as linear transformations.

Discusses a system identification and control method for complex systems from finite data. Effectiveness of the method for robust control; Formulation of the annihilation-correlation algorithms; Identification of the sample path based finite-time polynomial rate of convergence.

Considers the problem of designing a controller that minimizes the worst-case peak to peak gain of the closed loop system. Natural approach to the full state feedback problem based on dynamic programming; Finite horizon full state feedback; Infinite horizon version of the optimality and feasibility problems; Stabilizing suboptimal strategies.

Focuses on the use of the quadratic programming approach in solving the general multiblock l1 control problem, while identifying other methods including the finitely many equations approximation (FMV-FME) delay augmentation (DA) and the convex programming approach. Advantage of using the quadratic programming approach; Examination of the methods identified.

Presents a study which focuses on the requirements arising from the interaction of identification with robust control. What robust control presupposes; Use of problatistic and set-membership approaches; What the approach leads to.

Studies infinite-dimensional semidefinite programs (SP's), presenting a lifting technique to recast SP's as parameterized linear programs (LP's). Key to problems in optimal and robust control theory; Conditions for the lack of a duality gap for infinite-dimensional SP's; Basis of practical computation schemes for infinite-dimensional problems.

Investigates several multi-objective control problems resulting to equivalent convex optimization problems through the application of duality theory results. Application of uniform treatment essential in problem resolution; Links of problem complication with infinite-dimensional optimization problems; Interpretation of results derived from duality relationship.

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.