A System Level Approach to Controller Synthesis

Biological and advanced cyber-physical control systems 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 constrained controller design feasible and tractable. We introduce a new “system level” (SL) approach involving three complementary SL elements. SL parameterizations (SLPs) provide an alternative to the Youla parameterization of all stabilizing controllers and the responses they achieve, and combine with SL constraints (SLCs) to parameterize the largest known class of constrained stabilizing controllers that admit a convex characterization, generalizing quadratic invariance. SLPs also lead to a generalization of detectability and stabilizability, suggesting the existence of a rich separation structure, that when combined with SLCs is naturally applicable to structurally constrained controllers and systems. 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, and external system performance. Finally, we formulate SL synthesis problems, which define the broadest known class of constrained optimal control problems that can be solved using convex programming

System level parameterizations, constraints and synthesis

We introduce the system level approach to controller synthesis, which is composed of three elements: System Level Parameterizations (SLPs), System Level Constraints (SLCs) and System Level Synthesis (SLS) problems. SLPs provide a novel parameterization of all internally stabilizing controllers and the system responses that they achieve. These can be combined with SLCs to provide parameterizations of constrained stabilizing controllers. We provide a catalog of useful SLCs, and show that by using SLPs with SLCs, we can parameterize the largest known class of constrained stabilizing controllers that admit a convex characterization. Finally, we formulate the SLS problem, and show that it defines the broadest known class of constrained optimal control problems that can be solved using convex programming. We end by using the system level approach to computationally explore tradeoffs in controller performance, architecture cost, robustness and synthesis/implementation complexity

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 System Level Approach to Discrete-Time Nonlinear Systems

In this paper, we will show that there is a universal connection between the closed-loop and the corresponding realizing controller in nonlinear discrete-time systems: Given an achievable stable closed-loop, we can follow a systematic procedure to construct an internally stable causal controller that realizes the desired closed-loop. In the linear system case, this relationship has been used as a key result in the recently developed System Level Synthesis (SLS), and this paper shows how this relationship finds its analogue in the general nonlinear discrete-time system case. Necessary and sufficient conditions are presented that characterize the entire space of closedloops that are achievable by some causal controller for a given system. Furthermore, we will show that constructing the same causal controller from maps that are not achievable closed-loops, still can stabilize the nonlinear system if they approximate the feasibility conditions well enough. Finally, we will discuss how this method opens up new ways towards robust nonlinear controller synthesis, by exploring two direct applications of this approach: design of trajectory tracking controllers for nonlinear systems using linear SLS controllers, and a method to stably "blend" multiple linear SLS controllers into one nonlinear controller that improves closed-loop performance. The companion paper [1] applies the latter approach to large-scale systems with actuator saturation and safety constraints

A System Level Approach to Discrete-Time Nonlinear Systems

In this paper, we will show that there is a universal connection between the closed-loop and the corresponding realizing controller in nonlinear discrete-time systems: Given an achievable stable closed-loop, we can follow a systematic procedure to construct an internally stable causal controller that realizes the desired closed-loop. In the linear system case, this relationship has been used as a key result in the recently developed System Level Synthesis (SLS), and this paper shows how this relationship finds its analogue in the general nonlinear discrete-time system case. Necessary and sufficient conditions are presented that characterize the entire space of closedloops that are achievable by some causal controller for a given system. Furthermore, we will show that constructing the same causal controller from maps that are not achievable closed-loops, still can stabilize the nonlinear system if they approximate the feasibility conditions well enough. Finally, we will discuss how this method opens up new ways towards robust nonlinear controller synthesis, by exploring two direct applications of this approach: design of trajectory tracking controllers for nonlinear systems using linear SLS controllers, and a method to stably "blend" multiple linear SLS controllers into one nonlinear controller that improves closed-loop performance. The companion paper [1] applies the latter approach to large-scale systems with actuator saturation and safety constraints

Distributed Linear Quadratic Regulator Robust to Communication Dropouts

We present a solution to deal with information package dropouts in distributed controllers for large-scale networks. We do this by leveraging the System Level Synthesis approach, a control framework particularly suitable for large-scale networks that addresses information exchange in a very transparent manner. To this end, we propose two different schemes for controller synthesis and implementation. The first one synthesizes a controller inherently robust to dropouts, which is later implemented in an offline fashion. For the second approach, we synthesize a collection of controllers offline and then switch between different controllers online depending on the current dropouts detected in the system. The two approaches are illustrated and compared by means of a simulation example.Comment: Accepted contribution to the 21st World Congress of the International Federation of Automatic Control, 202