Introduction to algorithms
IEEE Journal on Selected Areas in Communications
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We describe an integrated modeling framework for an interactive power network (IPN) consisting of a power network (PN) and a wireless communication network (WCN). The PN is modeled using a set of piecewise linear (PWL) equations. The WCN is modeled using a Markov chain-based model that can capture the randomness of the communication channel. The impacts of the WCN are incorporated into the PN models using variable time delays. By formulating a convex optimization problem based on a composite Lyapunov function and solving this problem using linear matrix inequality solvers, we predict the reaching criteria for orbital existence. We investigate the impacts of time delays due to the wireless network and communication channel disruptions on the reachability bound, mean square stability, and performance of the IPN. Subsequently, using the integrated modeling framework, we demonstrate the efficacy of a scheme to jointly optimize control performance and network resource utilization. We demonstrate how communication fault tolerant protocols can be implemented to ensure that the IPNs operate within their reachability and performance bounds, despite one or more disruptions in the communication channels. We further demonstrate that when the WCN is clustered due to communication disruptions, each cluster can optimize its control communication network.