We consider a smart-grid connecting several agents, modeled as stochastic dynamical systems, who may be electricity consumers producers. At each discrete time instant, which may represent a 15 minute interval, each agent may consume generate some quantity of electrical energy. The Independent System Operator (ISO) is given the task of assigning consumptions generations to the agents so as to maximize the sum of the utilities accrued to the agents, subject to the constraint that energy generation equals consumption at each time. This task of coordinating generation and demand has to be accomplished by the ISO without the agents revealing their system states, dynamics, or utility cost functions. We show how and when a simple iterative procedure converges to the optimal solution. The ISO iteratively obtains electricity bids by the agents, and declares the tentative market clearing prices. In response to these prices, the agents submit new bids. On the demand side, the solution yields an optimal demand response for dynamic and stochastic loads. On the generation side, it provides the optimal utilization of stochastically varying renewables such as solar wind, and generation with fossil fuel based generation with dynamic constraints such as ramping rates. Thereby we solve a decentralized stochastic control problem, without agents sharing any information about their system models, states or utility functions.
We show below that the ISO Problem is an example of a decentralized control system with non-classical observation patterns in which signaling can successfully result in globally optimum performance. The agents need not reveal their observations, state values, their individual system dynamics or their individual cost-functions. We construct concrete signaling schemes which encode-decode the information required in order to recover the same performance as that of centralized control. From the economics side, this work is an extension of general equilibrium theory @cite_2 . To the authors' knowledge there does not appear to be any similar result for coordinating multiple LQG systems or the efficiency of the simplified signaling.
@cite_2
2034073776 2635604129 2142505627 2540490069 2015084328 2167485994 1787709854 2171153629 2588872972 2113385647 2074430484 2168150810 2615774546 2130343868 2072113937 1981109871 1982401839 2136157118 2163382065 2150704725
In this paper, the problem of feedback and active user selection in multiple-input single-output (MISO) wireless systems such that the system’s stability region is as big as possible is examined. The focus is on a system in a Rayleigh fading environment where zero forcing precoding is used to serve all active users in every slot. Acquisition of the channel states is done via uplink training in time division duplexing mode by the active users. Clearly, only a subset of users can perform uplink training and the selection of this subset is a challenging and interesting problem especially in MISO systems. The stability regions of a baseline centralized scheme and two novel decentralized policies are examined analytically. In the decentralized schemes, the transmitter broadcasts periodically the queue state information and the users contend for the channel in a carrier sense multiple access-based manner with parameters based on the outdated queue state information and real-time channel state information. We show that, using infrequent signaling between the base station and the users, the decentralized policies outperform the centralized policy. In addition, a threshold-based user selection and training scheme for discrete-time contention is proposed. The results of this paper imply that, as far as stability is concerned, the users must be involved in the active user selection and feedback training decision. This should be leveraged in future communication systems. This paper characterizes the performance in terms of queueing stability of a network composed of multiple MIMO transmitter-receiver pairs taking into account the dynamic traffic pattern and the probing feedback cost. We adopt a centralized scheduling scheme that selects a number of active pairs in each time-slot. We consider that the transmitters apply interference alignment (IA) technique if two or more pairs are active, whereas in the special case where one pair is active point-to-point MIMO singular value decomposition (SVD) is used. We consider a time-division duplex (TDD) system where transmitters acquire their channel state information (CSI) by decoding the pilot sequences sent by the receivers. Since global CSI knowledge is required for IA, the transmitters have also to exchange their estimated CSIs over a backhaul of limited capacity (i.e. imperfect case). Under this setting, we characterize in this paper the stability region of the system under both the imperfect and perfect (i.e. unlimited backhaul) cases, then we examine the gap between these two resulting regions. Further, under each case we provide a centralized probing policy that achieves the max stability region. These stability regions and scheduling policies are given for the symmetric system, where all the path loss coefficients are equal to each other, as well as for the general system. For the symmetric system, we provide the conditions under which IA yields a queueing stability gain compared to SVD. Under the general system, the adopted scheduling policy is of a high computational complexity for moderate numbers of pairs, consequently we propose an approximate policy that has a reduced complexity but that achieves only a fraction of the system stability region. A characterization of this fraction is provided. Decentralized control of cooperative systems captures the operation of a group of decision-makers that share a single global objective. The difficulty in solving optimally such problems arises when the agents lack full observability of the global state of the system when they operate. The general problem has been shown to be NEXP-complete. In this paper, we identify classes of decentralized control problems whose complexity ranges between NEXP and P. In particular, we study problems characterized by independent transitions, independent observations, and goal-oriented objective functions. Two algorithms are shown to solve optimally useful classes of goal-oriented decentralized processes in polynomial time. This paper also studies information sharing among the decision-makers, which can improve their performance. We distinguish between three ways in which agents can exchange information: indirect communication, direct communication and sharing state features that are not controlled by the agents. Our analysis shows that for every class of problems we consider, introducing direct or indirect communication does not change the worst-case complexity. The results provide a better understanding of the complexity of decentralized control problems that arise in practice and facilitate the development of planning algorithms for these problems. In this paper, we study resource allocation for a multicarrier-based cognitive radio (CR) network. More specifically, we investigate the problem of secondary users’ energy-efficiency (EE) maximization problem under secondary total power and primary interference constraints. First, assuming cooperation among the secondary base stations (BSs), a centralized approach is considered to solve the EE optimization problem for the CR network where the primary and secondary users are using either orthogonal frequency-division multiplexing (OFDM) or filter bank based multicarrier (FBMC) modulations. We propose an alternating-based approach to solve the joint power-subcarrier allocation problem. More importantly, in the first place, subcarriers are allocated using a heuristic method for a given feasible power allocation. Then, we conservatively approximate the nonconvex power control problem and propose a joint successive convex approximation-Dinkelbach algorithm (SCADA) to efficiently obtain a solution to the nonconvex power control problem. The proposed algorithm is shown to converge to a solution that coincides with the stationary point of the original nonconvex power control subproblem. Moreover, we propose a dual decomposition-based decentralized version of the SCADA. Second, under the assumption of no cooperation among the secondary BSs, we propose a fully distributed power control algorithm from the perspective of game theory. The proposed algorithm is shown to converge to a Nash-equilibrium (NE) point. Moreover, we propose a sufficient condition that guarantees the uniqueness of the achieved NE. Extensive simulation analyses are further provided to highlight the advantages and demonstrate the efficiency of our proposed schemes. We address the problem of designing decentralized feedback laws to force the outputs of decoupled nonlinear systems (agents) to follow geometric paths while holding a desired formation pattern. To this effect we propose a general framework that takes into account i) the topology of the communication links among the agents, ii) the fact that communications do not occur in a continuous manner, and iii) the cost of exchanging information. We provide conditions under which the resulting overall closed loop system is input-to-state stable and apply the methodology for two cases: agents with nonlinear dynamics in strict feedback form and a class of underactuated vehicles. Furthermore, we address explicitly the case where the communications among the agents occur with non-homogenous, possibly varying delays. A coordinated path-following algorithm is derived for multiple underactuated autonomous underwater vehicles. Simulation results are presented and discussed. This paper describes decentralized control laws for the coordination of multiple vehicles performing spatially distributed tasks. The control laws are based on a gradient descent scheme applied to a class of decentralized utility functions that encode optimal coverage and sensing policies. These utility functions are studied in geographical optimization problems and they arise naturally in vector quantization and in sensor allocation tasks. The approach exploits the computational geometry of spatial structures such as Voronoi diagrams. This paper introduces signaling in a global game so as to examine the informational role of policy in coordination environments such as currency crises and bank runs. While exogenous asymmetric information has been shown to select a unique equilibrium, we show that the endogenous information generated by policy interventions leads to multiple equilibria. The policy maker is thus trapped into a position in which self-fulfilling expectations dictate not only the coordination outcome but also the optimal policy. This result does not rely on the freedom to choose out-of-equilibrium beliefs, nor on the policy being a public signal; it may obtain even if the policy is observed with idiosyncratic noise. The paper studies asynchronous consensus problems of continuous-time multi-agent systems with discontinuous information transmission. The proposed consensus control strategy is implemented based on the state information of each agent's neighbors at some discrete times. The asynchrony means that each agent's update times, at which the agent adjusts its dynamics, are independent of others'. Furthermore, it is assumed that the communication topology among agents is time-dependent and the information transmission is with bounded time-varying delays. If the union of the communication topology across any time interval with some given length contains a spanning tree, the consensus problem is shown to be solvable. The analysis tool developed in this paper is based on nonnegative matrix theory and graph theory. The main contribution of this paper is to provide a valid distributed consensus algorithm that overcomes the difficulties caused by unreliable communication channels, such as intermittent information transmission, switching communication topology, and time-varying communication delays, and therefore has its obvious practical applications. Simulation examples are provided to demonstrate the effectiveness of the theoretical results. Consider a control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is to minimize a quadratic cost function in the state variables and control signal, known as the linear quadratic regulator (LQR). We study the fundamental tradeoff between the communication rate @math bits sec and the expected cost @math . We obtain a lower bound on a certain rate-cost function, which quantifies the minimum directed mutual information between the channel input and output that is compatible with a target LQR cost. The rate-cost function has operational significance in multiple scenarios of interest: among others, it allows us to lower-bound the minimum communication rate for fixed and variable length quantization, and for control over noisy channels. We derive an explicit lower bound to the rate-cost function, which applies to the vector, non-Gaussian, and partially observed systems, thereby extending and generalizing an earlier explicit expression for the scalar Gaussian system, due to Tatikonda el al. The bound applies as long as the system noise has a probability density function. It can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state. Via a separation principle between control and communication, similar results hold for causal lossy compression of additive noise Markov sources. Apart from standard dynamic programming arguments, our technical approach leverages the Shannon lower bound, develops new estimates for data compression with coding memory, and uses some recent results on high resolution variable-length vector quantization to prove that the new converse bounds are tight. We consider dynamic spectrum access where distributed secondary users search for spectrum opportunities without knowing the primary traffic statistics. In each slot, a secondary transmitter chooses one channel to sense and subsequently transmit if the channel is sensed as idle. Sensing is imperfect, i.e., an idle channel may be sensed as busy and vice versa. Without centralized control, each secondary user needs to independently identify the channels that offer the most opportunities while avoiding collisions with both primary and other secondary users. We address the problem within a cooperative game framework, where the objective is to maximize the throughput of the secondary network under a constraint on the collision with the primary system. The performance of a decentralized channel access policy is measured by the system regret, defined as the expected total performance loss with respect to the optimal performance in the ideal scenario where the traffic load of the primary system on each channel is known to all secondary users and collisions among secondary users are eliminated through centralized scheduling. By exploring the rich communication structure of the problem, we show that the optimal system regret has the same logarithmic order as in the centralized counterpart with perfect sensing. A decentralized policy is constructed to achieve the logarithmic order of the system regret. In a broader context, this work addresses imperfect reward observation in decentralized multi-armed bandit problems. This paper re-visits Shayevitz & Feder's recent ‘Posterior Matching Scheme’, an explicit, dynamical system encoder for communication with feedback that treats the message as a point on the [0,1] line and achieves capacity on memo-ryless channels. It has two key properties that ensure that it maximizes mutual information at each step: (a) the encoder sequentially hands the decoder what is missing; and (b) the next input has the desired statistics. Motivated by brain-machine interface applications and multi-antenna communications, we consider developing dynamical system feedback encoders for scenarios when the message point lies in higher dimensions. We develop a necessary and sufficient condition — the Jacobian equation — for any dynamical system encoder that maximizes mutual information. In general, there are many solutions to this equation. We connect this to the Monge-Kantorovich Optimal Transportation Problem, which provides a framework to identify a unique solution suiting a specific purpose. We provide two examplar capacity-achieving solutions — for different purposes — for the multi-antenna Gaussian channel with feedback. This insight further elucidates an interesting relationship between interactive decision theory problems and the theory of optimal transportation. In this contribution, the performance of an uplink CDMA system is analyzed in the context of frequency selective fading channels. Using game theoretic tools, a useful framework is provided in order to determine the optimal power allocation when users know only their own channel (while perfect channel state information is assumed at the base station). We consider the realistic case of frequency selective channels. This scenario illustrates the case of decentralized schemes and aims at reducing the downlink signaling overhead. Various receivers are considered, namely the Matched filter, the MMSE filter and the optimum filter. The goal of this paper is to derive simple expressions for the non-cooperative Nash equilibrium as the number of mobiles becomes large. To that end we combine two asymptotic methodologies. The first is asymptotic random matrix theory which allows us to obtain explicit expressions for the impact of all other mobiles on any given tagged mobile. The second is the theory of non-atomic games along with the Wardrop equilibrium concept which allows us to compute good approximations of the Nash equilibrium as the number of mobiles grow. We study the algorithmics of information structure design --- a.k.a. persuasion or signaling --- in a fundamental special case introduced by Arieli and Babichenko: multiple agents, binary actions, and no inter-agent externalities. Unlike prior work on this model, we allow many states of nature. We assume that the principal's objective is a monotone set function, and study the problem both in the public signal and private signal models, drawing a sharp contrast between the two in terms of both efficacy and computational complexity. When private signals are allowed, our results are largely positive and quite general. First, we use linear programming duality and the equivalence of separation and optimization to show polynomial-time equivalence between (exactly) optimal signaling and the problem of maximizing the objective function plus an additive function. This yields an efficient implementation of the optimal scheme when the objective is supermodular or anonymous. Second, we exhibit a (1-1 e)-approximation of the optimal private signaling scheme, modulo an additive loss of e, when the objective function is submodular. These two results simplify, unify, and generalize results of [Arieli and Babichenko, 2016] and [Babichenko and Barman, 2016], extending them from a binary state of nature to many states (modulo the additive loss in the latter result). Third, we consider the binary-state case with a submodular objective, and simplify and slightly strengthen the result of [Babichenko and Barman, 2016] to obtain a (1-1 e)-approximation via a scheme which (i) signals independently to each receiver and (ii) is "oblivious" in that it does not depend on the objective function so long as it is monotone submodular. When only a public signal is allowed, our results are negative. First, we show that it is NP-hard to approximate the optimal public scheme, within any constant factor, even when the objective is additive. Second, we show that the optimal private scheme can outperform the optimal public scheme, in terms of maximizing the sender's objective, by a polynomial factor. In this paper a novel approach to the problem of decentralized agreement toward a common point in space in a multi-agent system is proposed. Our method allows the agents to agree on the relative location of the network centroid respect to themselves, on a common reference frame and therefore on a common heading. Using this information a global positioning system for the agents using only local measurements can be achieved. In the proposed scenario, an agent is able to sense the distance between itself and its neighbors and the direction in which it sees its neighbors with respect to its local reference frame. Furthermore only point-to-point asynchronous communications between neighboring agents are allowed thus achieving robustness against random communication failures. The proposed algorithms can be thought as general tools to locally retrieve global information usually not available to the agents. In the traffic assignment problem, first proposed by Wardrop in 1952, commuters select the shortest available path to travel from their origins to their destinations. We study a generalization of this problem in which competitors, who may control a nonnegligible fraction of the total flow, ship goods across a network. This type of games, usually referred to as atomic games, readily applies to situations in which the competing freight companies have market power. Other applications include intelligent transportation systems, competition among telecommunication network service providers, and scheduling with flexible machines. Our goal is to determine to what extent these systems can benefit from some form of coordination or regulation. We measure the quality of the outcome of the game without centralized control by computing the worst-case inefficiency of Nash equilibria. The main conclusion is that although self-interested competitors will not achieve a fully efficient solution from the system's point of view, the loss is not too severe. We show how to compute several bounds for the worst-case inefficiency that depend on the characteristics of cost functions and on the market structure in the game. In addition, building upon the work of Catoni and Pallotino, we show examples in which market aggregation (or collusion) adversely impacts the aggregated competitors, even though their market power increases. For example, Nash equilibria of atomic network games may be less efficient than the corresponding Wardrop equilibria. When competitors are completely symmetric, we provide a characterization of the Nash equilibrium using a potential function, and prove that this counterintuitive phenomenon does not arise. Finally, we study a pricing mechanism that elicits more coordination from the players by reducing the worst-case inefficiency of Nash equilibria. This paper proposes a decentralized interference control scheme for an OFDMA (Orthogonal Frequency Division Multiple Access) cellular scenario where multiple macrocells and femtocells are deployed. In particular, we model the distributed resource allocation problem by means of a potential game, which is demonstrated to converge to a unique and pure Nash equilibrum. In this game, the femto base stations are the players, their actions are the resource blocks and the corresponding power levels to be allocated for downlink transmission, and the utility is designed to guarantee coexistence with the macro system, guaranteeing a fair tradeoff between femto and macro systems' performances. To do that, the utility function does not only consider the capacity of the femtocells, but also the different sources of inter-system interference: macrocell to femtocell, femtocell to femtocell, and femtocell to macrocell. The game is solved by applying a better response dynamic, which first selects the best resource blocks allocation policy for the femtousers, and then selects the most appropriate power levels for each resource block, through the solution of the corresponding convex optimization problem. Simulation results show that the introduction of femtocells in the scenario increases the total system capacity, and that the considered utility function provides an improvement in macro system performance of up to 40 , while reducing the femto capacity only up to 7 , with respect to the well known iterative waterfilling game. This paper reviews the classical decentralized decision theory in the light of new constraints and requirements. The central theme that transcends various aspects of signal processing design is that an integrated channel-aware approach needs to be taken for optimal detection performance given the available resources. Recent publications recognize that decentralized algorithms useful in wireless data applications can be obtained via microeconomics and game theory. In these studies, each agent maximizes, under appropriate rules and constraints, a quality-of-service (QoS) index. A key solution is a "Nash equilibrium"; i.e., an allocation from which no agent is better off by unilaterally "deviating". The actual maximization may be made by software which may not be directly "controllable" by a human user. The model and, especially, the chosen QoS index should be as general as possible, so that the derived results be applicable to a wide variety of channel conditions, modulation schemes, and other physical-layer characteristics. Likewise, the chosen index should exhibit predictable and reliable technical behavior, without exacting a high complexity cost. This note describes a model, and particularly, a QoS index which can accommodate a wide variety of physical layer situations. The proposed index is shown to exhibit solid technical behavior, be physically significant, intuitively appealing, and applicable to a wide variety of physical layer situations. A game in which terminals carrying multi-rate traffic seek to maximize this index is analyzed, and closed-form equilibrium conditions and power levels are derived "from first principles". All terminals want the same signal-to-interference ratio (SIR), but some cannot reach the necessary power level. At equilibrium, a number of terminals transmit full power, and others achieve the same optimal SIR. A basic rationale to search for these equilibria is provided. In a decentralized hypothesis testing network, several peripheral nodes observe an environment and communicate their observations to a central node for the final decision. The presence of capacity constraints introduces theoretical and practical problems. The following problem is addressed: given that the peripheral encoders that satisfy these constraints are scalar quantizers, how should they be designed in order that the central test to be performed on their output indices is most powerful? The scheme is called cooperative design-separate encoding since the quantizers process separate observations but have a common goal; they seek to maximize a system-wide performance measure. The Bhattacharyya distance of the joint index space as such a criterion is suggested, and a design algorithm to optimize arbitrarily many quantizers cyclically is proposed. A simplified version of the algorithm, namely an independent design-separate encoding scheme, where the correlation is either absent or neglected for the sake of simplicity, is outlined. Performances are compared through worked examples. > In the average consensus a set of linear systems has to be driven to the same final state, which corresponds to the average of their initial states. This mathematical problem can be seen as the simplest example of coordination task. In fact it can be used to model both the control of multiple autonomous vehicles which all have to be driven to the centroid of the initial positions, and to model the decentralized estimation of a quantity from multiple measure coming from distributed sensors. This contribution presents a consensus strategy in which the systems can exchange information among themselves according to a fixed strongly connected digital communication network. Beside the decentralized computational aspects induced by the choice of the communication network, we here have also to face the quantization effects due to the digital links. We here present and discuss two different encoding decoding strategies with theoretical and simulation results on their performance. Copyright © 2009 John Wiley & Sons, Ltd.