Split-as-a-Pro: behavioral control via operator splitting and alternating projections
Yu Tang, Carlo Cenedese, Alessio Rimoldi, Florian Dórfler, John Lygeros, Alberto Padoan
TL;DR
Split-as-a-Pro addresses the scalability gap in dynamic optimization for control by marrying behavioral systems theory with operator splitting and alternating projections to reduce optimization to modular projections. It introduces monotone-inclusion reformulations (two- and three-operator) and corresponding splitting schemes (Forward-Backward and Davis–Yin), then replaces hard projections onto a constraint set with distributed alternating projections onto simpler sets, enabling gray-box and data-driven representations. In numerical studies on scalable interconnected systems and constrained receding-horizon tasks, the distributed Split-as-a-Pro variants outperform centralized solvers in runtime while preserving performance and feasibility under interconnection and input/output constraints. The framework thus enables scalable, flexible, and structure-exploiting control for large-scale networks and mixed model/data representations, with potential broad applicability to dynamic optimization problems.
Abstract
The paper introduces Split-as-a-Pro, a control framework that integrates behavioral systems theory, operator splitting methods, and alternating projection algorithms. The framework reduces dynamic optimization problems - arising in both control and estimation - to efficient projection computations. Split-as-a-Pro builds on a non-parametric formulation that exploits system structure to separate dynamic constraints imposed by individual subsystems from external ones, such as interconnection constraints and input/output constraints. This enables the use of arbitrary system representations, as long as the associated projection is efficiently computable, thereby enhancing scalability and compatibility with gray-box modeling. We demonstrate the effectiveness of Split-as-a-Pro by developing a distributed algorithm for solving finite-horizon linear quadratic control problems and illustrate its use in predictive control. Our numerical case studies show that algorithms obtained using Split-as-a-Pro significantly outperform their centralized counterparts in runtime and scalability across various standard graph topologies, while seamlessly leveraging both model-based and data-driven system representations.