Farzad Salehisadaghiani

Distributed connectivity preservation of a team of single integrator agents subject to measurement error

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.

Distributed Nash equilibrium seeking in networked graphical games

Abstract This paper considers a gossip approach for finding a Nash equilibrium in networked games on graphs, where a player’s cost function may be affected by the actions of any subset of players. An interference graph illustrates the partially-coupled cost functions, i.e., the asymmetric strategic interaction and information requirements. An algorithm is proposed whereby players make decisions based only on the estimates of their interfering players’ actions. Given the interference graph (not necessarily complete), a communication graph is designed so that players exchange only their required information. When the interference graph is sparse, the algorithm can offer substantial savings in communication and computation. Almost sure convergence to a Nash equilibrium is proved for diminishing step sizes. The effect of the second largest eigenvalue of the expected communication matrix on the convergence rate is quantified.

Nash Equilibrium Seeking with Non-doubly Stochastic Communication Weight Matrix

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, there is no exact convergence. Then, we present an almost sure convergence proof of the algorithm to a Nash equilibrium of the game. Moreover, 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.

Formation control of a team of single-integrator agents with measurement error

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.