System Level Synthesis

This article surveys the System Level Synthesis framework, which presents a novel perspective on constrained robust and optimal controller synthesis for linear systems. We show how SLS shifts the controller synthesis task from the design of a controller to the design of the entire closed loop system, and highlight the benefits of this approach in terms of scalability and transparency. We emphasize two particular applications of SLS, namely large-scale distributed optimal control and robust control. In the case of distributed control, we show how SLS allows for localized controllers to be computed, extending robust and optimal control methods to large-scale systems under practical and realistic assumptions. In the case of robust control, we show how SLS allows for novel design methodologies that, for the first time, quantify the degradation in performance of a robust controller due to model uncertainty -- such transparency is key in allowing robust control methods to interact, in a principled way, with modern techniques from machine learning and statistical inference. Throughout, we emphasize practical and efficient computational solutions, and demonstrate our methods on easy to understand case studies.Comment: To appear in Annual Reviews in Contro

A modified AAA algorithm for learning stable reduced-order models from data

In recent years, the Adaptive Antoulas-Anderson AAA algorithm has established itself as the method of choice for solving rational approximation problems. Data-driven Model Order Reduction (MOR) of large-scale Linear Time-Invariant (LTI) systems represents one of the many applications in which this algorithm has proven to be successful since it typically generates reduced-order models (ROMs) efficiently and in an automated way. Despite its effectiveness and numerical reliability, the classical AAA algorithm is not guaranteed to return a ROM that retains the same structural features of the underlying dynamical system, such as the stability of the dynamics. In this paper, we propose a novel algebraic characterization for the stability of ROMs with transfer function obeying the AAA barycentric structure. We use this characterization to formulate a set of convex constraints on the free coefficients of the AAA model that, whenever verified, guarantee by construction the asymptotic stability of the resulting ROM. We suggest how to embed such constraints within the AAA optimization routine, and we validate experimentally the effectiveness of the resulting algorithm, named stabAAA, over a set of relevant MOR applications.Comment: 29 pages, 4 figures. With respect to the previous version: typos have been corrected and an appendix has been adde

Data-Driven Control of Stochastic Systems: An Innovation Estimation Approach

Recent years have witnessed a booming interest in the data-driven paradigm for predictive control. However, under noisy data ill-conditioned solutions could occur, causing inaccurate predictions and unexpected control behaviours. In this article, we explore a new route toward data-driven control of stochastic systems through active offline learning of innovation data, which gives an answer to the critical question of how to derive an optimal data-driven model from a noise-corrupted dataset. A generalization of the Willems' fundamental lemma is developed for non-parametric representation of input-output-innovation trajectories, provided realizations of innovation are precisely known. This yields a model-agnostic unbiased output predictor and paves the way for data-driven receding horizon control, whose behaviour is identical to the ``oracle" solution of certainty-equivalent model-based control with measurable states. For efficient innovation estimation, a new low-rank subspace identification algorithm is developed. Numerical simulations show that by actively learning innovation from input-output data, remarkable improvement can be made over present formulations, thereby offering a promising framework for data-driven control of stochastic systems

Regularization and Bayesian Learning in Dynamical Systems: Past, Present and Future

Regularization and Bayesian methods for system identification have been repopularized in the recent years, and proved to be competitive w.r.t. classical parametric approaches. In this paper we shall make an attempt to illustrate how the use of regularization in system identification has evolved over the years, starting from the early contributions both in the Automatic Control as well as Econometrics and Statistics literature. In particular we shall discuss some fundamental issues such as compound estimation problems and exchangeability which play and important role in regularization and Bayesian approaches, as also illustrated in early publications in Statistics. The historical and foundational issues will be given more emphasis (and space), at the expense of the more recent developments which are only briefly discussed. The main reason for such a choice is that, while the recent literature is readily available, and surveys have already been published on the subject, in the author's opinion a clear link with past work had not been completely clarified.Comment: Plenary Presentation at the IFAC SYSID 2015. Submitted to Annual Reviews in Contro