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Structured Feedback Optimization for Metzler Dynamics

Anderson, James and Murray, Riley (2018) Structured Feedback Optimization for Metzler Dynamics. In: 2018 IEEE Conference on Decision and Control (CDC). IEEE , Piscataway, NJ, pp. 4417-4424. ISBN 978-1-5386-1395-5.

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We propose a method to compute convergent lower bounds for the state-feedback controller design problem Inf/F {L(F):A+BF is Metzler & stable} where L is a convex loss function of F . The theory behind the approach is simple: relying only on an extension of Perron-Frobenius to Metzler matrices, and popular discrete optimization techniques. The method itself has two tuning parameters (which enable faster recovery of solutions, with possible introduction of optimality gaps) and is practical for systems with a non-trivial state dimension. A convergence result with respect to the optimal solution is derived, and a direct heuristic algorithm based on linear programming is given. We explain how projecting A onto the set of stable Metzler matrices is essentially the hardest of these problems, and focus our numerical examples on precisely this case.

Item Type:Book Section
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Anderson, James0000-0002-2832-8396
Additional Information:© 2018 IEEE. JA is supported by NSF grants CCF 1637598 and ECCS 1619352 and DTRA grant HDTRA 1-15-1-003. RM is supported by funding from grants NSF AitF-1637598 and CPS-154471.
Funding AgencyGrant Number
Defense Threat Reduction Agency (DTRA)HDTRA 1-15-1-003
Record Number:CaltechAUTHORS:20190204-160454036
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Official Citation:J. Anderson and R. Murray, "Structured Feedback Optimization for Metzler Dynamics," 2018 IEEE Conference on Decision and Control (CDC), FL, USA, 2018, pp. 4417-4424. doi: 10.1109/CDC.2018.8618672
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92642
Deposited By: Tony Diaz
Deposited On:05 Feb 2019 01:06
Last Modified:16 Nov 2021 03:52

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