The past few years have witnessed a revolution in data collection capabilities: The development of low cost, ultra low power sensors capable of harvesting energy from the environment has rendered ubiquitous sensing feasible. When coupled with a parallel growth in actuation capabilities, these developments open up the possibility of new control applications that can profoundly impact society, ranging from zero-emissions buildings to ``smart" grids and managed aquifers to achieve long term sustainable use of scarce resources. A major road-block to realizing this vision stems from the curse of dimensionality. To successfully operate in these scenarios, controllers will need to timely extract relevant, actionable information from the very large data streams generated by the ubiquitous sensors. However, existing techniques are ill-equipped to deal with this "data avalanche."
This talk discusses the central role that systems theory can play in developing computationally tractable, scalable methods for extracting actionable information that is very sparsely encoded in high dimensional data streams. The key insight is the realization that actionable information can be often represented with a small number of invariants associated with an underlying dynamical system. Thus, in this context, the problem of actionable information extraction can be reformulated as identifying these invariants from (high dimensional) noisy data, and thought of as a generalization of sparse signal recovery problems to a dynamical systems framework. While in principle this approach leads to generically nonconvex, hard to solve problems, computationally tractable relaxations (and in some cases exact solutions) can be obtained by exploiting a combination of elements from convex analysis and the classical theory of moments. These ideas will be illustrated using examples from several application domains, including autonomous vehicles, computer vision, systems biology and economics. We will conclude the talk by exploring the connection between hybrid systems identification, information extraction, and machine learning, and point out to new research directions in systems theory motivated by these problems.