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Controllability of Linear Dynamical Systems under Input Sparsity Constraints

Joseph, G and Murthy, CR (2021) Controllability of Linear Dynamical Systems under Input Sparsity Constraints. In: IEEE Transactions on Automatic Control, 66 (2). pp. 924-931.

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Official URL: https://dx.doi.org/10.1109/TAC.2020.2989245


In this article, we consider the controllability of a discrete-time linear dynamical system with sparse control inputs. Sparsity constraints on the input arises naturally in networked systems, where activating each input variable adds to the cost of control. We derive algebraic necessary and sufficient conditions for ensuring controllability of a system with an arbitrary transfer matrix. The derived conditions can be verified in polynomial time complexity, unlike the more traditional Kalman-type rank tests. Further, we characterize the minimum number of input vectors required to satisfy the derived conditions for controllability. Finally, we present a generalized Kalman decomposition-like procedure that separates the state-space into subspaces corresponding to sparse-controllable and sparse-uncontrollable parts. These results form a theoretical basis for designing networked linear control systems with sparse inputs. © 1963-2012 IEEE.

Item Type: Journal Article
Publication: IEEE Transactions on Automatic Control
Publisher: Institute of Electrical and Electronics Engineers Inc.
Additional Information: The copyright of this article belongs to Institute of Electrical and Electronics Engineers Inc.
Keywords: Controllability; Dynamical systems; Linear control systems; Networked control systems; Polynomial approximation; Transfer matrix method, Discrete time linear dynamical systems; Input variables; Kalman decompositions; Linear dynamical systems; Networked systems; Polynomial time complexity; Sparse controls; Sparsity constraints, Discrete time control systems
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 26 Feb 2021 06:25
Last Modified: 26 Feb 2021 06:25
URI: http://eprints.iisc.ac.in/id/eprint/68005

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