Split-as-a-Pro: behavioral control via operator splitting and alternating projections

TL;DR

Split-as-a-Pro is a control framework that simplifies dynamic optimization in control and estimation by using operator splitting and projections, improving scalability and efficiency especially for large systems.

Contribution

It introduces a non-parametric, structure-exploiting control framework that enables scalable, distributed solutions for dynamic optimization problems in control systems.

Findings

Distributed algorithms outperform centralized ones in runtime and scalability.

Framework effectively integrates model-based and data-driven representations.

Demonstrated success in predictive control with various graph topologies.

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.