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Guoqiang Hu

Publications and source records attributed to Guoqiang Hu.

51 records · Page 3Linked to original sources

Distributed Nash Equilibrium Seeking for Monotone Generalized Noncooperative Games by a Regularized Penalty Method

In this work, we study the distributed Nash equilibrium seeking problem for monotone generalized noncooperative games with set constraints and shared affine inequality constraints. A distributed regularized penalty method is proposed. The idea is to use a differentiable penalty function with a time-varying penalty parameter to deal with the inequality constraints. A time-varying regularization term is used to deal with the ill-poseness caused by the monotonicity assumption and the time-varying penalty term. The asymptotic convergence to the least-norm variational equilibrium of the game is proven. Numerical examples show the effectiveness and efficiency of the proposed algorithm.

math.OC↗

A Continuous-Time Nesterov Accelerated Gradient Method for Centralized and Distributed Online Convex Optimization

This paper studies the online convex optimization problem by using an Online Continuous-Time Nesterov Accelerated Gradient method (OCT-NAG). We show that the continuous-time dynamics generated by the online version of the Bregman Lagrangian achieves a constant static regret $\frac{c}σ$ independent of $T$, provided that some boundedness assumptions on the objective functions and optimal solutions hold. To the best of the authors' knowledge, this is the lowest static regret in the literature (lower than $O(\text{log}(T))$). We further show that under the same assumptions, the dynamic regret of the algorithm is $O(T)$, which is comparable with the existing methods. Simulation results validate the effectiveness and efficiency of the method. Furthermore, the simulation shows that the algorithm performs well in terms of the dynamic regret for some specific scaling conditions. In addition, we consider the application of the proposed online optimization method in distributed online optimization problems, and show that the proposed algorithm achieves an $O(\sqrt{T})$ static regret, which is comparable with the existing distributed online optimization methods. Different from these methods, the proposed method requires neither the gradient boundedness assumption nor the compact constraint set assumption, which allows different objective functions and different optimization problems with those in the literature. A comparable dynamic regret is obtained. Simulation results show the effectiveness and efficiency of the distributed algorithm.

math.OC↗

Attack-Resilient Distributed Algorithms for Exponential Nash Equilibrium Seeking

This paper investigates a resilient distributed Nash equilibrium (NE) seeking problem on a directed communication network subject to malicious cyber-attacks. The considered attacks, named as Denial-of-Service (DoS) attacks, are allowed to occur aperiodically, which refers to interruptions of communication channels carried out by intelligent adversaries. In such an insecure network environment, the existence of cyber-attacks may result in undesirable performance degradations or even the failures of distributed algorithm to seek the NE of noncooperative games. Hence, the aforementioned setting can improve the practical relevance of the problem to be addressed and meanwhile, it poses some technical challenges to the distributed algorithm design and exponential convergence analysis. In contrast to the existing distributed NE seeking results over a prefect communication network, an attack-resilient distributed algorithm is presented such that the NE can be exactly reached with an exponential convergence rate in the presence of DoS attacks. Inspired by the previous works in [21]-[26], an explicit analysis of the attack frequency and duration is investigated to enable exponential NE seeking with resilience against attacks.Examples and numerical simulation results are given to show the effectiveness of the proposed design.

eess.SY↗

Prescribed-Time Fully Distributed Nash Equilibrium Seeking in Noncooperative Games

In this paper, we investigate a prescribed-time and fully distributed Nash Equilibrium (NE) seeking problem for continuous-time noncooperative games. By exploiting pseudo-gradient play and consensus-based schemes, various distributed NE seeking algorithms are presented over either fixed or switching communication topologies so that the convergence to the NE is reached in a prescribed time. In particular, a prescribed-time distributed NE seeking algorithm is firstly developed under a fixed graph to find the NE in a prior-given and user-defined time, provided that a static controller gain can be selected based on certain global information such as the algebraic connectivity of the communication graph and both the Lipschitz and monotone constants of the pseudo-gradient associated with players' objective functions. Secondly, a prescribed-time and fully distributed NE seeking algorithm is proposed to remove global information by designing heterogeneous dynamic gains that turn on-line the weights of the communication topology. Further, we extend this algorithm to accommodate jointly switching topologies. It is theoretically proved that the global convergence of those proposed algorithms to the NE is rigorously guaranteed in a prescribed time based on a time function transformation approach. In the last, numerical simulation results are presented to verify the effectiveness of the designs.

eess.SY↗

Distributed Nash Equilibrium Seeking with Limited Cost Function Knowledge via A Consensus-Based Gradient-Free Method

This paper considers a distributed Nash equilibrium seeking problem, where the players only have partial access to other players' actions, such as their neighbors' actions. Thus, the players are supposed to communicate with each other to estimate other players' actions. To solve the problem, a leader-following consensus gradient-free distributed Nash equilibrium seeking algorithm is proposed. This algorithm utilizes only the measurements of the player's local cost function without the knowledge of its explicit expression or the requirement on its smoothness. Hence, the algorithm is gradient-free during the entire updating process. Moreover, the analysis on the convergence of the Nash equilibrium is studied for the algorithm with both diminishing and constant step-sizes, respectively. Specifically, in the case of diminishing step-size, it is shown that the players' actions converge to the Nash equilibrium almost surely, while in the case of fixed step-size, the convergence to the neighborhood of the Nash equilibrium is achieved. The performance of the proposed algorithm is verified through numerical simulations.

math.OC↗

Adaptive Approaches for Fully Distributed Nash Equilibrium Seeking in Networked Games

This paper considers the design of fully distributed Nash equilibrium seeking strategies for multi-agent games. To develop fully distributed seeking strategies, two adaptive control laws, including a node-based control law and an edge-based control law, are proposed. In the node-based adaptive strategy, each player adjusts their own weight on their procurable consensus error dynamically. Moreover, in the edge-based algorithm, the fully distributed strategy is designed by adjusting the weights on the edges of the communication graph adaptively. By utilizing LaSalle's invariance principle, it is shown that the Nash equilibrium is globally asymptotically stable by both strategies given that the players' objective functions are twice-continuously differentiable, the partial derivatives of the players' objective functions with respect to their own actions are globally Lipschitz, the pseudo-gradient vector of the game is strongly monotone and the communication network is undirected and connected. In addition, we further show that the edge-based method can be easily adapted to accommodate time-varying communication conditions, in which the communication network is switching among a set of undirected and connected graphs. In the last, a numerical example is given to illustrate the effectiveness of the proposed methods.

math.OC↗

Differentially private Nash equilibrium seeking for networked aggregative games

This paper considers the privacy-preserving Nash equilibrium seeking strategy design for a class of networked aggregative games, in which the players' objective functions are considered to be sensitive information to be protected. In particular, we consider that the networked game is free of central node and the aggregate information is not directly available to the players. As there is no central authority to provide the aggregate information required by each player to update their actions, a dynamic average consensus protocol is employed to estimate it. To protect the players' privacy, we perturb the transmitted information among the players by independent random noises drawn from Laplace distributions. By synthesizing the perturbed average consensus protocol with a gradient algorithm, distributed privacy-preserving Nash equilibrium seeking strategies are established for the aggregative games under both fixed and time-varying communication topologies. With explicit quantifications of the mean square errors, the convergence results of the proposed methods are presented. Moreover, it is analytically proven that the proposed algorithm is $ε$-differentially private, where $ε$ depends on the stepsize of the gradient algorithm and the scaling parameter of the random variables. The presented results indicate that there is a tradeoff between the convergence accuracy and the privacy level. Lastly, a numerical example is provided for the verification of the proposed methods.

math.OC↗

A Unified Strategy for Solution Seeking in Graphical N-coalition Noncooperative Games

This paper aims to reduce the communication and computation costs of the Nash equilibrium seeking strategy for the $N$-coalition noncooperative games proposed in [1]. The objective is achieved in two manners: 1. An interference graph is introduced to describe the interactions among the agents in each coalition. 2. The Nash equilibrium seeking strategy is designed with the interference graphs considered. The convergence property of the proposed Nash equilibrium seeking strategy is analytically investigated. It is shown that the agents' actions generated by the proposed method converge to a neighborhood of the Nash equilibrium of the graphical $N$-coalition noncooperative games under certain conditions. Several special cases where there is only one coalition and/or there are coalitions with only one agent are considered. The results for the special cases demonstrate that the proposed seeking strategy achieves the solution seeking for noncooperative games, social cost minimization problems and single-agent optimization problems in a unified framework. Numerical examples are presented to support the theoretical results.

math.OC↗

HVAC Energy Cost Optimization for a Multi-zone Building via a Decentralized Approach

It has been well acknowledged that buildings account for a large proportion of the world's energy consumption. However, the energy use of buildings, especially the heating, ventilation and air-conditioning (HVAC), is far from being efficient. There still exists a dramatic potential to save energy through improving building energy efficiency. Therefore, this paper studies the control of HVAC system for multi-zone buildings with the objective to reduce energy consumption cost while satisfying thermal comfort. In particular, the thermal couplings due to the heat transfer between the adjacent zones are incorporated in the optimization. Considering that a centralized method is generally computationally prohibitive for large buildings, an efficient decentralized approach is developed, based on the Accelerated Distributed Augmented Lagrangian (ADAL) method [1]. To evaluate the performance of the proposed method, we first compare it with a centralized method, in which the optimal solution of a small-scale problem can be obtained. We find that this decentralized approach can almost approach the optimal solution of the problem. Further, this decentralized approach is compared with the Distributed Token-Based Scheduling Strategy (DTBSS) [2]. The numeric results reveal that when the number of zones is relatively small (less than 20), the two decentralized methods can achieve a comparable performance regarding the cost of the HVAC system. However, with an increase of the number of zones in the building, the proposed decentralized approach demonstrates better performance with a considerable reduction of the total cost. Moreover, the decentralized approach proposed in this paper demonstrate better scalability with less average computation required.

eess.SY↗

A New Approach to Linear/Nonlinear Distributed Fusion Estimation Problem

Disturbance noises are always bounded in a practical system, while fusion estimation is to best utilize multiple sensor data containing noises for the purpose of estimating a quantity--a parameter or process. However, few results are focused on the information fusion estimation problem under bounded noises. In this paper, we study the distributed fusion estimation problem for linear time-varying systems and nonlinear systems with bounded noises, where the addressed noises do not provide any statistical information, and are unknown but bounded. When considering linear time-varying fusion systems with bounded noises, a new local Kalman-like estimator is designed such that the square error of the estimator is bounded as time goes to $\infty$. A novel constructive method is proposed to find an upper bound of fusion estimation error, then a convex optimization problem on the design of an optimal weighting fusion criterion is established in terms of linear matrix inequalities, which can be solved by standard software packages. Furthermore, according to the design method of linear time-varying fusion systems, each local nonlinear estimator is derived for nonlinear systems with bounded noises by using Taylor series expansion, and a corresponding distributed fusion criterion is obtained by solving a convex optimization problem. Finally, target tracking system and localization of a mobile robot are given to show the advantages and effectiveness of the proposed methods.

eess.SY↗

Economic MPC of Nonlinear Systems with Non-Monotonic Lyapunov Functions and Its Application to HVAC Control

This paper proposes a Lyapunov-based economic MPC scheme for nonlinear sytems with non-monotonic Lyapunov functions. Relaxed Lyapunov-based constraints are used in the MPC formulation to improve the economic performance. These constraints will enforce a Lyapunov decrease after every few steps. Recursive feasibility and asymptotical convergence to the steady state can be achieved using Lyapunov-like stability analysis. The proposed economic MPC can be applied to minimize energy consumption in HVAC control of commercial buildings. The Lyapunov-based constraints in the online MPC problem enable the tracking of the desired set-point temperature. The performance is demonstrated by a virtual building composed of two adjacent zones.

eess.SY↗

Distributed Nash Equilibrium Seeking by A Consensus Based Approach

In this paper, Nash equilibrium seeking among a network of players is considered. Different from many existing works on Nash equilibrium seeking in non-cooperative games, the players considered in this paper cannot directly observe the actions of the players who are not their neighbors. Instead, the players are supposed to be capable of communicating with each other via an undirected and connected communication graph. By a synthesis of a leader-following consensus protocol and the gradient play, a distributed Nash equilibrium seeking strategy is proposed for the non-cooperative games. Analytical analysis on the convergence of the players' actions to the Nash equilibrium is conducted via Lyapunov stability analysis. For games with non-quadratic payoffs, where multiple isolated Nash equilibria may coexist in the game, a local convergence result is derived under certain conditions. Then, a stronger condition is provided to derive a non-local convergence result for the non-quadratic games. For quadratic games, it is shown that the proposed seeking strategy enables the players' actions to converge to the Nash equilibrium globally under the given conditions. Numerical examples are provided to verify the effectiveness of the proposed seeking strategy.

math.OC↗

Game Design and Analysis for Price based Demand Response: An Aggregate Game Approach

In this paper, an aggregate game approach is proposed for the modeling and analysis of energy consumption control in smart grid. Since the electricity user's cost function depends on the aggregate load, which is unknown to the end users, an aggregate load estimator is employed to estimate it. Based on the communication among the users about their estimations on the aggregate load, Nash equilibrium seeking strategies are proposed for the electricity users. By using singular perturbation analysis and Lyapunov stability analysis, a local convergence result to the Nash equilibrium is presented for the energy consumption game that may have multiple Nash equilibria. For the energy consumption game with a unique Nash equilibrium, it is shown that the players' strategies converge to the Nash equilibrium non-locally. More specially, if the unique Nash equilibrium is an inner Nash equilibrium, then the convergence rate can be quantified. Energy consumption game with stubborn players is also investigated. Convergence to the best response strategies for the rational players is ensured. Numerical examples are provided to verify the effectiveness of the proposed methods.

econ.GN↗

A Virtual Queue Approach for Online Estimation of Loss Probability Based on MVA Theory

In network quality of service provisioning, premium services generally require to keep a very small loss probability, which is infeasible to measure directly. The proposed virtual queue scheme estimates the small packet loss probability of a real queueing system by measuring queue statistics in a set of separate virtual queues. A novel scaling property between the real queue and the virtual queues is deduced on the basis of the maximum variance asymptotic (MVA) theory. The new scheme retains the high accuracy and wide applicability of the MVA method for aggregated traffic while avoiding the high computational complexity in a direct application of the original MVA analysis in real time. This makes it suitable for online measurement applications such as network performance monitoring and measurement-based admission control.

cs.NI↗

Performance Modeling and Evaluation for Information-Driven Networks

Information-driven networks include a large category of networking systems, where network nodes are aware of information delivered and thus can not only forward data packets but may also perform information processing. In many situations, the quality of service (QoS) in information-driven networks is provisioned with the redundancy in information. Traditional performance models generally adopt evaluation measures suitable for packet-oriented service guarantee, such as packet delay, throughput, and packet loss rate. These performance measures, however, do not align well with the actual need of information-driven networks. New performance measures and models for information-driven networks, despite their importance, have been mainly blank, largely because information processing is clearly application dependent and cannot be easily captured within a generic framework. To fill the vacancy, we present a new performance evaluation framework particularly tailored for information-driven networks, based on the recent development of stochastic network calculus. We analyze the QoS with respect to information delivery and study the scheduling problem with the new performance metrics. Our analytical framework can be used to calculate the network capacity in information delivery and in the meantime to help transmission scheduling for a large body of systems where QoS is stochastically guaranteed with the redundancy in information.

cs.PF↗