Most cyber–physical systems (CPS) encounter a large volume of data which is added to the system gradually in real time and not altogether in advance. In this paper, we provide a theoretical framework that yields optimal control strategies for such CPS at the intersection of control theory and learning. In the proposed framework, we use the actual CPS, i.e., the ‘‘true" system that we seek to optimally control online, in parallel with a model of the CPS that is available. We then institute an information state for the system which does not depend on the control strategy. An important consequence of this independence is that for any given choice of a control strategy and a realization of the system’s variables until time t, the information states at future times do not depend on the choice of the control strategy at time t but only on the realization of the decision at time t, and thus they are related to the concept of separation between estimation of the state and control. Namely, the future information states are separated from the choice of the current control strategy. Such control strategies are called separated control strategies. Hence, we can derive offline the optimal control strategy of the system with respect to the information state, which might not be precisely known due to model uncertainties or complexity of the system, and then use standard learning approaches to learn the information state online while data are added gradually to the system in real time. We show that after the information state becomes known, the separated control strategy of the CPS model derived offline is optimal for the actual system. We illustrate the proposed framework in a dynamic system consisting of two subsystems with a delayed sharing information structure.
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Large-Scale System Identification Using a Randomized SVD
Learning a dynamical system from input/output data is a fundamental task in the control design pipeline. In the partially observed setting there are two components to identification: parameter estimation to learn the Markov parameters, and system realization to obtain a state space model. In both sub-problems it is implicitly assumed that standard numerical algorithms such as the singular value decomposition (SVD) can be easily and reliably computed. When trying to fit a high-dimensional model to data, even computing an SVD may be intractable. In this work we show that an approximate matrix factorization obtained using randomized methods can replace the standard SVD in the realization algorithm while maintaining the finite-sample performance and robustness guarantees of classical methods.
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- Award ID(s):
- 2144634
- NSF-PAR ID:
- 10390335
- Date Published:
- Journal Name:
- Proceedings of the 2022 American Control Conference (ACC)
- Page Range / eLocation ID:
- 2178 to 2185
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/ACC53348.2022.9867836
