A Stochastic Robust Adaptive Systems Level Approach to Stabilizing Large-Scale Uncertain Markovian Jump Linear Systems

Abstract: We propose a unified framework for robustly and adaptively stabilizing large-scale networked uncertain Markovian jump linear systems (MJLS) under external disturbances and mode switches that can change the network's topology. Adaptation is achieved by using minimal information on the disturbance to identify modes that are consistent with observable data. Robust control is achieved by extending the system level synthesis (SLS) approach, which allows us to pose the problem of simultaneously stabilizing multiple plants as a two-step convex optimization procedure. Our control pipeline computes a likelihood distribution of the system's current mode, uses them as probabilistic weights during simultaneous stabilization, then updates the likelihood via Bayesian inference. Because of this "softer" probabilistic approach to robust stabilization, our control pipeline does not suffer from abrupt destabilization issues due to changes in the system's true mode, which were observed in a previous method. Separability of SLS also lets us compute localized robust controllers for each subsystem, allowing for network scalability; we use several information consensus methods so that mode estimation can also be done locally. We apply our algorithms to disturbance-rejection on two sample dynamic power grid networks, a small-scale system with 7 nodes and a large-scale grid of 25 nodes.