A System Level Approach to Controller Synthesis (1610.04815v3)

Abstract: Biological and advanced cyberphysical 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. System Level Parameterizations (SLPs) generalize state space and Youla parameterizations of all stabilizing controllers and the responses they achieve, and combine with System Level Constraints (SLCs) to parameterize the largest known class of constrained stabilizing controllers that admit a convex characterization, generalizing quadratic invariance (QI). 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. 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 example illustrates how this system level approach can systematically explore tradeoffs in controller performance, robustness, and synthesis/implementation complexity.

• The paper introduces System Level Parameterizations as a flexible alternative to Youla, enabling stabilizing controllers under structural constraints.
• It generalizes quadratic invariance by proposing convex System Level Constraints that accommodate sparse, delay, and locality restrictions.
• The novel controller realization maps system responses to internal dynamics, ensuring scalable implementation for distributed cyber-physical systems.

A System Level Approach to Controller Synthesis

The paper "A System Level Approach to Controller Synthesis" by Yuh-Shyang Wang, Nikolai Matni, and John C. Doyle presents a sophisticated framework for addressing controller synthesis in complex cyber-physical systems plagued by constraints such as limited communication, uncertain sensing, and distributed computing. The authors propose a "system level" (SL) approach involving the integration of System Level Parameterizations (SLPs), System Level Constraints (SLCs), and System Level Synthesis (SLS) to construct stabilizing controllers that leverage structured plants and performance requirements.

Key Contributions

1. System Level Parameterizations (SLPs): The paper introduces SLPs as an alternative to the widely used Youla parameterization. SLPs offer a parameterization of all stabilizing controllers and the closed-loop responses they achieve, extending the flexibility to accommodate structural and sparsity constraints. This approach allows for the characterization of controllers that is more general than existing methods like quadratic invariance (QI).
2. Convex Generalization of Quadratic Invariance: A major highlight is the generalization beyond QI by introducing SLCs. This provides a convex characterization of the largest known class of constrained stabilizing controllers, facilitating the synthesis of controllers under sparse, delay, and locality constraints that were previously infeasible with QI alone.
3. Novel Controller Realization: The authors offer a unique realization for implementing the control law, which enhances transparency and scalability. The controller structure proposed in the paper maps the system response to internal controller dynamics directly, ensuring that constraints imposed on system responses map naturally to the controller implementation.
4. System Level Synthesis (SLS) Problems: The formulation of SLS problems encompasses the broadest known class of constrained optimal control problems solvable using convex programming. This includes all previous distributed optimal control problems within the QI framework. SLS problems incorporate a wide range of constraints, allowing for exploration of trade-offs between controller performance, robustness, and implementation complexity.

Strong Numerical Results and Implications

The proposed methodology demonstrates strong applicability across a number of illustrative examples, notably in decentralized control scenarios where communication delays may traditionally hinder convex optimization methods. The SLS approach handles these delays effectively, enabling localized control implementations by leveraging sparse system responses. The paper argues convincingly that the feasibility of configuring such sparse constraints translates directly into ensuring controller implementability at scale, transforming the complexity landscape of large-scale system design.

Future Directions

The implications for future developments in AI and complex systems are profound. The SL approach could guide research into autonomous systems with distributed control, enhancing robustness and efficiency in fields such as robotics and energy systems. The framework likely paves the way for further exploration into decentralized architectures beyond traditional top-down control approaches, fostering advancements in networked system designs. Moreover, the ability to synthesize controllers optimizing for multiple objectives opens pathways for interdisciplinary applications requiring nuanced control mechanisms.

This paper establishes a significant foundation for evolving control theory in the face of modern challenges presented by cyber-physical, biological, and distributed systems. Its methodical approach to convex synthesis under a novel parameterization framework places it at the forefront of research fostering practical solutions to real-world control system difficulties.