RSRG Seminar

In the 90s, robust and optimal control theory had a significant impact on application areas such as aerospace and process control.  This was because this theory provided both strong mathematical guarantees of system performance and robustness, as well as the computational tools needed to make these theoretical guarantees actionable by domain experts.  The problems arising in the areas initially targeted by robust and optimal control could all be cast as that of synthesizing a single logically centralized controller for a single system.  In contrast, advanced cyberphysical and biological systems, such as the smart gird, software defined networks, the Internet of Things, intelligent transportation systems, and the human sensorimotor system, have dramatically different characteristics, introducing novel technical, theoretical and computational challenges to the controller synthesis task.  In particular, biological and advanced cyberphysical control systems, in addition to being large-scale, often have limited, sparse, uncertain, and distributed communication and computing in addition to sensing and actuation.  Fortunately, the corresponding plants and performance requirements are also sparse and structured, and this must be exploited to make controller design for these systems feasible and tractable. To do so, we revisit, rethink and generalize foundational concepts of robust and optimal control theory, and introduce a new "system level" (SL) approach to constrained optimal/robust controller synthesis involving three complementary SL elements. System Level Parameterizations (SLPs) generalize the classical state space and Youla parameterizations of all stabilizing controllers and the responses that they achieve, and combine with System Level Constraints (SLCs) to parameterize the largest known class of constrained (e.g., distributed) stabilizing controllers that admit a convex characterization.  We further provide a catalog of useful SLCs, most importantly including sparsity, delay, and locality constraints on both communication and computing internal to the controller, controller architecture complexity, and external system performance. The resulting System Level Synthesis (SLS) problems that arise define the broadest known class of constrained optimal control problems that can be solved using convex programming.  An important class of constrained optimal controllers that can only now be synthesized using convex programming are those that satisfy certain spatiotemporal locality properties — we explain why locality is essential to scale the synthesis and implementation of optimal controllers to systems of arbitrary size, and illustrate the power of this approach by synthesizing, in minutes using only a single laptop, a distributed optimal controller for a system with 51000 states.  The SL approach to controller synthesis thus provides a unified, tractable and scalable set of tools for the design of large-scale cyberphyiscal systems.  As an illustration of the power of these methods, we end with an application of SLS to a power-system inspired example, and illustrate how our approach can be used to systematically explore tradeoffs in controller performance, robustness, architectural complexity and synthesis/implementation complexity.