Unified Approach to Convex Robust Distributed Control given Arbitrary Information Structures

We consider the problem of computing optimal linear control policies for linear systems in finite-horizon. The states and the inputs are required to remain inside pre-specified safety sets at all times despite unknown disturbances. In this technical note, we focus on the requirement that the control policy is distributed, in the sense that it can only be based on partial information about the history of the outputs. It is well-known that when a condition denoted as Quadratic Invariance (QI) holds, the optimal distributed control policy can be computed in a tractable way. Our goal is to unify and generalize the class of information structures over which quadratic invariance is equivalent to a test over finitely many binary matrices. The test we propose certifies convexity of the output-feedback distributed control problem in finite-horizon given any arbitrarily defined information structure, including the case of time varying communication networks and forgetting mechanisms. Furthermore, the framework we consider allows for including polytopic constraints on the states and the inputs in a natural way, without affecting convexity

Reducing Cascading Failure Risk by Increasing Infrastructure Network Interdependency

Increased coupling between critical infrastructure networks, such as power and communication systems, will have important implications for the reliability and security of these systems. To understand the effects of power-communication coupling, several have studied interdependent network models and reported that increased coupling can increase system vulnerability. However, these results come from models that have substantially different mechanisms of cascading, relative to those found in actual power and communication networks. This paper reports on two sets of experiments that compare the network vulnerability implications resulting from simple topological models and models that more accurately capture the dynamics of cascading in power systems. First, we compare a simple model of topological contagion to a model of cascading in power systems and find that the power grid shows a much higher level of vulnerability, relative to the contagion model. Second, we compare a model of topological cascades in coupled networks to three different physics-based models of power grids coupled to communication networks. Again, the more accurate models suggest very different conclusions. In all but the most extreme case, the physics-based power grid models indicate that increased power-communication coupling decreases vulnerability. This is opposite from what one would conclude from the coupled topological model, in which zero coupling is optimal. Finally, an extreme case in which communication failures immediately cause grid failures, suggests that if systems are poorly designed, increased coupling can be harmful. Together these results suggest design strategies for reducing the risk of cascades in interdependent infrastructure systems