Abstract
The ideas of controllable and unobservable subspaces of a linear dynamical system introduced by Kalman play a central role in the theory of control systems. They determine, among other aspects, the existence of solutions to many control problems of interest. Analogous to the notions of controllable and unobservable subspaces are the notions of “securable” and “unsecurable” subspace of a linear dynamical system, which have operational significance in the context of secure control. We examine what guarantees can be provided with respect to securable subspace, especially in the case when there is process noise in the system.
This material is based upon work partially supported by NSF under Contract Nos. ECCS-1646449, ECCS-1547075, CCF-1619085 and Science & Technology Center Grant CCF-0939370, the U.S. Army Research Office under Contract No. W911NF-15-1-0279, the Power Systems Engineering Research Center (PSERC), and NPRP grant NPRP 8-1531-2-651 from the Qatar National Research Fund, a member of Qatar Foundation.
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Notes
- 1.
More generally, this could be generalized to a martingale difference sequence with a one-step ahead conditional covariance that is uniformly bounded below by a positive definite matrix.
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Satchidanandan, B., Kumar, P. (2018). Control Systems Under Attack: The Securable and Unsecurable Subspaces of a Linear Stochastic System. In: Tempo, R., Yurkovich, S., Misra, P. (eds) Emerging Applications of Control and Systems Theory. Lecture Notes in Control and Information Sciences - Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-67068-3_16
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DOI: https://doi.org/10.1007/978-3-319-67068-3_16
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