Introduction to Nonlinear Systems, ECE1647 & Dynamic Systems and Control, ECE311 & Systems Control, ECE557
Teaching Assistant of Prof. Lacra Pavel, Dr. Tome Kosteski and Prof. Manfredi Maggiore, University of Toronto.
He received his B.Sc. degree from Amirkabir University of Technology, Tehran, Iran, and his M.A.Sc. degree from Concordia University, Montreal, Canada, both in Electrical Engineering. He is currently a Ph.D. student at the University of Toronto, Canada in the systems control group. His research interests include Nash Equilibrium seeking using iterative algorithms in distributed networks and distributed control of multi-agent systems.
Research Assistant
University of Toronto, Systems Control Group
Research Assistant
Concordia University, Department of Electrical and Computer Engineering
Ph.D. in Electrical Engineering
University of Toronto, Toronto, Canada
Master of Applied Science in Electrical Engineering
Concordia University, Montreal, Canada
Bachelor of Science in Electrical Engineering
Amirkabir University of Technology, Tehran, Iran
In the problem of finding a Nash equilibrium of a game in a distributed multi-player network, each player (agent) pursues the minimization of his cost function selfishly by taking a proper action in response to other players. Thus each player requires the full information of all other players actions in the network. However, in a distributed network this is a stringent requirement. These distributed networks usually consist of different entities which do not belong to a single authority and they may pursue different/opposite interests. The consequences of lack of information oblige players to minimize their cost functions based on the limited local information received from the neighboring players which is obtained through a communication graph. The objective is to design an algorithm to find a NE of the game over the communication graph.
A generalization to this problem is to consider the interactions between the players which are not described by a complete graph (i.e., the players' cost functions may be affected by the actions of any subset of players, not necessarily all the players). We denote this graph of interactions by Interference Graph. Communication is assumed limited and a communication graph, which is a subset of the interference graph, is designed for the network. Our objective here is to generalize the algorithm for computing a NE of the game with partially coupled cost functions as described by the interference graph using only imperfect information over the communication graph.
This paper considers a distributed gossip approach for finding a Nash equilibrium in networked games on graphs. In such games a player's cost function may be affected by the actions of any subset of players. An interference graph is employed to illustrate the partially-coupled cost functions and the asymmetric information requirements. For a given interference graph, network communication between players is considered to be limited. A generalized communication graph is designed so that players exchange only their required information. An algorithm is designed whereby players, with possibly partially-coupled cost functions, make decisions based on the estimates of other players' actions obtained from local neighbors. It is shown that this choice of communication graph guarantees that all players' information is exchanged after sufficiently many iterations. Using a set of standard assumptions on the cost functions, the interference and the communication graphs, almost sure convergence to a Nash equilibrium is proved for diminishing step sizes. Moreover, the case when the cost functions are not known by the players is investigated and a convergence proof is presented for diminishing step sizes. The effect of the second largest eigenvalue of the expected communication matrix on the convergence rate is quantified. The trade-off between parameters associated with the communication graph and the ones associated with the interference graph is illustrated. Numerical results are presented for a large-scale networked game.
A distributed Nash equilibrium seeking algorithm is presented for networked games. We assume an incomplete information available to each player about the other players' actions. The players communicate over a strongly connected digraph to send/receive the estimates of the other players' actions to/from the other local players according to a gossip communication protocol. Due to asymmetric information exchange between the players, a non-doubly (row) stochastic weight matrix is defined. We show that, due to the non-doubly stochastic property, the total average of all players' estimates is not preserved for the next iteration which results in having no exact convergence. We present an almost sure convergence proof of the algorithm to a Nash equilibrium of the game. Then, we extend the algorithm for graphical games in which all players' cost functions are only dependent on the local neighboring players over an interference digraph. We design an assumption on the communication digraph such that the players are able to update all the estimates of the players who interfere with their cost functions. It is shown that the communication digraph needs to be a superset of a transitive reduction of the interference digraph. Finally, we verify the efficacy of the algorithm via a simulation on a social media behavioral case.
In this paper, the problem of finding a Nash equilibrium of a multi-player game is considered. The players are only aware of their own cost functions as well as the action space of all players. We develop a relatively fast algorithm within the framework of inexact-ADMM. It requires a communication graph for the information exchange between the players as well as a few mild assumptions on cost functions. The convergence proof of the algorithm to a Nash equilibrium of the game is then provided. Moreover, the convergence rate is investigated via simulations.
We consider a gossip approach for finding a Nash equilibrium in a distributed multi-player network game. We extend previous results on Nash equilibrium seeking to the case when the players' cost functions may be affected by the actions of any subset of players. An interference graph is employed to illustrate the partially-coupled cost functions and the asymmetric information requirements. For a given interference graph, we design a generalized communication graph so that players with possibly partially-coupled cost functions exchange only their required information and make decisions based on them. Using a set of standard assumptions on the cost functions, interference and communication graphs, we prove almost sure convergence to a Nash equilibrium for diminishing step sizes. We then quantify the effect of the second largest eigenvalue of the expected communication matrix on the convergence rate, and illustrate the trade-off between the parameters associated with the communication and the interference graphs. Finally, the efficacy of the proposed algorithm on a large-scale networked game is demonstrated via simulation.
This paper presents an asynchronous gossip-based algorithm for finding a Nash equilibrium (NE) of a game in a distributed multi-player network. The algorithm is designed in such a way that players make decisions based on estimates of the other players' actions obtained from local neighbors. Using a set of standard assumptions on the cost functions and communication graph, the paper proves almost sure convergence to a NE for diminishing step sizes. For constant step sizes an error bound on expected distance from a NE is established. The effectiveness of the proposed algorithm is demonstrated via simulation for both diminishing and constant step sizes.
This paper deals with the connectivity preservation of multi-agent systems with state-dependent error in distance measurement. It is assumed that upper bounds on the measurement error and also its rate of change as a function of distance are available. A general class of distributed control strategies is then proposed for the distance-dependent connectivity preservation of the agents in the network. It is shown that if two neighboring agents are initially located at a distance closer than the required connectivity range, they are guaranteed to remain in the connectivity range at all times. The effectiveness of the proposed control strategies in consensus and containment problems is demonstrated by simulation.
This paper investigates the formation control problem for a team of single-integrator agents subject to distance measurement error. Collision, obstacle and boundary avoidance are important features of the proposed strategy. It is assumed that upper bounds exist on the magnitude of the measurement error and its derivative w.r.t. the measured distance. A decentralized navigation function is then proposed to move the agents toward a desired final configuration which is defined based on the pairwise distances of the connected agents and the characteristics of the distance measurement error. Conditions on the magnitude of the measurement error and its derivative w.r.t. the measured distance are derived under which a new formation configuration can be achieved anywhere in the space due to the measurement error. This error-dependent formation can be determined exactly if the error model is available. If such a model is not available, the maximum discrepancy in the final distances can be obtained in terms of the maximum measurement error. Moreover, the control law designed based on the navigation function ensures collision, obstacle and boundary avoidance in the workspace. The efficacy of the proposed control strategy is demonstrated by simulation.
Any cooperative control scheme relies on some measurements which are often assumed to be exact to simplify the analysis. However, it is known that in practice all measured quantities are subject to error, which can deteriorate the overall performance of the network significantly. This work proposes a new measurement error analysis in the control of multi-agent systems. In particular, the connectivity preservation of multi-agent systems with state-dependent error in distance measurements is considered. It is assumed that upper bounds on the measurement error and its rate of change are available. A general class of distributed control strategies is then proposed for the distance-dependent connectivity preservation of the agents in the network. It is shown that if two neighboring agents are initially located in the connectivity range, they are guaranteed to remain connected at all times. Furthermore, the formation control problem for a team of single-integrator agents subject to distance measurement error is investigated using navigation functions. Collision, obstacle and boundary avoidance are important features of the proposed strategy. Conditions on the magnitude of the measurement error and its rate of change are derived under which a new error-dependent formation can be achieved anywhere in the space. The effectiveness of the proposed control strategies in consensus and containment problems is demonstrated by simulation.
In this paper an asynchronous gossip-based algorithm is proposed for finding a Nash equilibrium of a game in a distributed multi-player network. The algorithm is designed in such a way that the players' actions are updated based on the estimates of the other players' actions which are obtained from the local neighbors. The almost sure convergence proof of the algorithm to a Nash equilibrium is provided under a set of standard assumptions on the cost functions and the communication graph. The effectiveness of the proposed algorithm is demonstrated via simulation.
Teaching Assistant of Prof. Lacra Pavel, Dr. Tome Kosteski and Prof. Manfredi Maggiore, University of Toronto.
Teaching Assistant of Dr. Mohamed Helwa, University of Toronto.
Teaching Assistant of Prof. Luca Scardovi, University of Toronto.
Teaching Assistant of Prof. Luca Scardovi, University of Toronto.
Teaching Assistant of Prof. Luca Scardovi and Prof. Manfredi Maggiore, University of Toronto.
Teaching Assistant of Prof. Luca Scardovi, University of Toronto.
Teaching Assistant of Prof. Manfredi Maggiore, University of Toronto.
Teaching Assistant of Prof. Mireille Broucke, University of Toronto.
Teaching Assistant of Prof. Lacra Pavel, University of Toronto.
Teaching Assistant of Prof. Aishy Amer, Concordia University.
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