In this paper, we considered a differential game theoretic approach to compute optimal strategies by a team of UAVs to evade the attack of an aerial jammer on the communication channel. We considered two variants of the problem in this paper. We formulated the problem as a zero-sum pursuit-evasion game and used Isaacs' approach to derive the necessary conditions to arrive at the equations governing the saddle-point strategies of the players. The cost function was picked as the termination time of the game. We illustrated the results through simulations.

In this paper, we have considered a differential game theoretic approach to compute optimal strategies by a team of vehicles to evade the attack of a jammer on the communication channel in a vehicular network with heterogenous dynamics. We formulated the problem as a zero-sum pursuit-evasion game and provide extension for Isaacs' approach to derive necessary conditions to arrive at the equations governing the saddle-point strategies of the multi-player zero-sum differential games. The cost function was picked as the termination time of the game. Finally, we derived the equations governing the optimal controls for the vehicles in case of a UAV and AGV and provide simulation results for the trajectories emanating out of the terminal manifold.

In this work, we generalized our previous work in \cite{sbhattac10} to networks having an arbitrary number of agents possessing different dynamics. We modeled the problem from the perspective of maintaining connectivity in a dynamic graph in which the existence of an edge between two nodes depends on the state of the nodes as well as the jammer. Due to the dependence of the combinatorial structure of the graph on the continuous-time dynamics of the nodes we used the notion of state-dependent graphs to model the problem. Applying tools from algebraic graph theory on the state-dependent graphs provided us with locally optimal control strategies for the agents as well as the jammer.

In this work, we investigated a jamming attack on the communication network of a team of UAVs flying in a formation. We proposed a communication and motion model for the UAVs. The communication model provided a relation in the spatial domain for effective jamming by an aerial intruder. We analysed a scenario in which multiple aerial intruders try to jam a communication channel among UAVs flying in a formation. We formulated the problem of jamming as a zero-sum pursuit-evasion game. We analyzed the problem in the framework of differential game theory, and used Isaacs' approach to compute the saddle-point strategies of the UAVs as well as the jammers. Finally we used tools from algebraic graph theory to characterize the termination manifold.

We investigate a jamming attack on the communication network of a multi-agent system in a formation. We propose a communication and motion model for the agents. The communication model provides a relation in the spatial domain for effective jamming by an intruder. We formulate the problem as a zero-sum pursuit-evasion game. In our earlier work we used Isaacs¡¯ approach to obtain motion strategies for a network of agents to evade the jamming attack. In this work, we imagine a scenario in which each agent has a knowledge about the value function under perfect state information, beforehand. Due to lack of information about all the agents in the team each agent is constrained to make a local decision based on the information about his neighbors. We propose online algorithms under decentralized information patterns which converge for each player. We propose approximation algorithms for the agents, based on averaging and provide some bounds on their performance.

In the following paper, we explore the concept of designing estimators for the agents. Under decentralized information structure, we study the performance of the entire formation when each agent runs an estimator based on the underlying information pattern in order to compute its actions. The performance measure considered in this work is the maximum time for which the network remains connected. We show that the convergence of the estimation error of one agent depends on the estimation error of the other agents, and the control law plays a dual role in such a scenario.

In this work, we study the problem of power allocation in teams. Each team consists of two agents who try to split their available power between the tasks of communication and jamming the nodes of the other team. The agents have constraints on their total energy and instantaneous power usage. The cost function is the difference between the rates of erroneously transmitted bits of each team. We model the problem as a zero-sum differential game between the two teams and use Isaacs¡¯ approach to obtain the necessary conditions for the optimal trajectories. This leads to a continuous-kernel power allocation game among the players. Based on the communications model, we present sufficient conditions on the physical parameters of the agents for the existence of a pure strategy Nash equilibrium (PSNE). Finally, we present simulation results for the case when the agents are holonomic.

In this work, we study the problem of power allocation and adaptive modulation in teams of decision makers. We model the adaptive modulation problem as a zero-sum matrix game which in turn gives rise to a a continuous kernel game to handle power control. Based on the communications model, we present sufficient conditions on the physical parameters of the agents for the existence of a pure strategy saddle-point equilibrium (PSSPE).

Contrary to our earlier work, this paper addresses the scenario in which each player has an omni-directional antenna for jamming the communication between the members of the other team. The agents have constraints on their total energy and instantaneous power usage. The cost function adopted is the difference between the rates of erroneously transmitted bits of each team. We model the problem as a zero-sum differential game between the two teams and use Isaacs¡¯ approach to obtain the necessary conditions for the optimal trajectories. We model the adaptive modulation problem as a zero-sum matrix game which in turn gives rise to a continuous kernel game to handle power control. Based on the communications model, we present sufficient conditions on the physical parameters of the agents for the existence of a pure strategy saddle-point equilibrium (PSSPE). This leads to a switching behavior in the optimal communication strategy within a team, over the time horizon of the entire game. This behavior is illustrated in our simulations for the case when the agents are holonomic.

In this work, we study the problem of power allocation and adaptive modulation in teams of decision makers. We consider the special case of two teams with each team consisting of two mobile agents. Agents belonging to the same team communicate over wireless ad hoc networks, and they try to split their available power between the tasks of communication and jamming the nodes of the other team. The agents have constraints on their total energy and instantaneous power usage. The cost function adopted is the difference between the rates of erroneously transmitted bits of each team. We model the adaptive modulation problem as a zero-sum matrix game which in turn gives rise to a a continuous kernel game to handle power control. Based on the communications model, we present sufficient conditions on the physical parameters of the agents for the existence of a pure strategy saddle-point equilibrium (PSSPE).

In this paper, we address the issue of malicious intrusion in the communication network present in a team of autonomous vehicles. In our current scenario, we consider the special case of two teams with each team consisting of two mobile agents. Agents belonging to the same team communicate over wireless ad hoc networks, and they try to split their available power between the tasks of communication and jamming the nodes of the other team. Contrary to our earlier work, this paper addresses the scenario in which each player has an omni-directional antenna for jamming the communication between the members of the other team. The agents have constraints on their total energy and instantaneous power usage. The cost function adopted is the difference between the rates of erroneously transmitted bits of each team. We model the problem as a zero-sum differential game between the two teams and use Isaacs¡¯ approach to obtain the necessary conditions for the optimal trajectories. We model the adaptive modulation problem as a zero-sum matrix game which in turn gives rise to a continuous kernel game to handle power control. Based on the communications model, we present sufficient conditions on the physical parameters of the agents for the existence of a pure strategy saddle-point equilibrium (PSSPE). This leads to a switching behavior in the optimal communication strategy within a team, over the time horizon of the entire game. This behavior is illustrated in our simulations for the case when the agents are holonomic.

In this paper, we study the tradeoff in resource allocation between malicious intrusion (jamming) and communication/coordination by two teams of mobile agents. Agents belonging to the same team communicate over wireless ad hoc networks, and they distribute their available power between the tasks of communication and jamming the communication network nodes of the other team. This is a generalization of our earlier work in [1] which considered the special case when each team consists of only two agents. Here we consider the non-trivial extension to multiple agents (in each team). The agents have constraints on their total energy and instantaneous power usage. The cost function @incollectionadopted is the difference between the rates of erroneously transmitted bits of each team. We model the problem as a zero-sum differential game between the two teams (where the teams are the actual players in the zero-sum game) and use Isaacs' approach to obtain necessary conditions for the corresponding trajectories. The solution to the optimal control problem for each team in turn depends on the solution to the power allocation problem for each agent. The power allocation problem is a non-zero sum game between the two teams, and we present sufficient conditions for the existence of a pure strategy Nash equilibrium. Finally, we provide some simulation results to validate the approach taken.