Proximal algorithms for large-scale statistical modeling and optimal sensor/actuator selection

Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The first, in statistical modeling, seeks to reconcile observed statistics by suitably and minimally perturbing prior dynamics. The second seeks to optimally select a subset of available sensors and actuators for control purposes. To address modeling and control of large-scale systems we develop a unified algorithmic framework using proximal methods. Our customized algorithms exploit problem structure and allow handling statistical modeling, as well as sensor and actuator selection, for substantially larger scales than what is amenable to current general-purpose solvers. We establish linear convergence of the proximal gradient algorithm, draw contrast between the proposed proximal algorithms and alternating direction method of multipliers, and provide examples that illustrate the merits and effectiveness of our framework. Index Terms Actuator selection, sensor selection, sparsity-promoting estimation and control, method of multipliers, nonsmooth convex optimization, proximal algorithms, regularization for design, semi-definite programming, structured covariances. I. INTRODUCTION Convex optimization has had tremendous impact on many disciplines, including system identification and control design [1]-[7]. The present paper focuses on two representative control problems, statistical control-oriented modeling and sensor/actuator selection, that are cast as convex programs.