Abstract
Many real-world control systems, such as the smart grid and software defined networks, have decentralized components that react quickly using local information and centralized components that react slowly using a more global view. This work seeks to provide a theoretical framework for how to design controllers that are decomposed across timescales in this way. The framework is analogous to how the network utility maximization framework uses optimization decomposition to distribute a global control problem across independent controllers, each of which solves a local problem; except our goal is to decompose a global problem temporally, extracting a timescale separation. Our results highlight that decomposition of a multi-timescale controller into a fast timescale, reactive controller and a slow timescale, predictive controller can be near-optimal in a strong sense. In particular, we exhibit such a design, named Multi-timescale Reflexive Predictive Control (MRPC), which maintains a per-timestep cost within a constant factor of the offline optimal in an adversarial setting.
- D. Cai, E. Mallada, and A. Wierman. Distributed optimization decomposition for joint economic dispatch and frequency regulation. In Decision and Control (CDC), 2015 IEEE 54th Annual Conference on, pages 15--22. IEEE, 2015.Google ScholarCross Ref
- M. Chiang, S. H. Low, A. R. Calderbank, and J. C. Doyle. Layering as optimization decomposition: A mathematical theory of network architectures. Proceedings of the IEEE, 95(1):255--312, 2007.Google ScholarCross Ref
- G. Goel, N. Chen, and A. Wierman. Thinking Fast and Slow: Optimization Decomposition Across Timescales. arXiv:1704.07785, Apr. 2017.Google Scholar
- D. Kreutz, F. M. Ramos, P. E. Verissimo, C. E. Rothenberg, S. Azodolmolky, and S. Uhlig. Software-defined networking: A comprehensive survey. Proceedings of the IEEE, 103(1):14--76, 2015.Google ScholarCross Ref
- S. H. Low, F. Paganini, and J. C. Doyle. Internet congestion control. IEEE control systems, 22(1):28--43, 2002.Google Scholar
- G. M. Masters. Renewable and efficient electric power systems. John Wiley & Sons, 2013.Google Scholar
- E. D. Sontag. Mathematical control theory: deterministic finite dimensional systems, volume 6. Springer Science & Business Media, 2013.Google Scholar
- R. Srikant. The mathematics of Internet congestion control. Springer Science & Business Media, 2012. Google ScholarDigital Library
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