Cooperative Design of Systems of Systems Against Attack on One Subsystem

Future large-scale control systems will be cyberphysical System of Systems (SoS)s each consisting of many interacting subsystems operating harmoniously and making decisions that benefit the entire enterprise. In terms of accomplishing their own objectives, the subsystems in an SoS will be designed so that their decision-making process achieves a Nash equilibrium for the entire SoS. This equilibrium ensures that no one subsystem can improve its position by deviating from the agreed decision. One of the weaknesses of this equilibrium is that it is vulnerable to cyber-attacks directed towards the objectives of one subsystem. In this paper, we consider an attack on a linear quadratic SoS that consists of altering some parameters in the objective function of one subsystem by injecting negative definite matrices into the attacked subsystem's objective function. Such an attack would be designed to disrupt the operation of the entire SoS by pitting one subsystem against the others and causing a change in the behavior and trajectory of the entire SoS. We consider two possible outcomes of the attack. The first is when the attack is not detected and all subsystems continue to operate as designed but now reaching a different Nash equilibrium that may or may not yield the outcome desired by the attacker. In this case, existence results related to the new Nash equilibrium will be derived. The second is when the attack is detected causing the remaining subsystems to react by forming a cooperative team to counter the actions of the attacked subsystem. The team will then establish a new Nash equilibrium with the attacked subsystem. Both of these possible outcomes of the cyber-attack will be analyzed. A 3-subsystems SoS example illustrating the results will also be presented. This example illustrates the ability of an attacker to drive the SoS's state trajectory away from the origin if the attack on one subsystem is not detected. It also illustrates the advantage that the remaining subsystems have in restoring the trajectory to one that is close to the pre-attack equilibrium trajectory by cooperating as a team if the attack is detected.