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Distributed LQR Methods for Networks of Non-Identical Plants

Vlahakis, E. E. & Halikias, G. ORCID: 0000-0003-1260-1383 (2019). Distributed LQR Methods for Networks of Non-Identical Plants. In: 2018 IEEE Conference on Decision and Control (CDC). 2018 IEEE Conference on Decision and Control (CDC), 17-19 Dec. 2018, Miami Beach, FL, USA. doi: 10.1109/cdc.2018.8619185


Two well-established complementary distributed linear quadratic regulator (LQR) methods applied to networks of identical agents are extended to the non-identical dynamics case. The first uses a top-down approach where the centralized optimal LQR controller is approximated by a distributed control scheme whose stability is guaranteed by the stability margins of LQR control. The second consists of a bottom-up approach in which optimal interactions between self-stabilizing agents are defined so as to minimize an upper bound of the global LQR criterion. In this paper, local state-feedback controllers are designed by solving model-matching type problems and mapping all the agents in the network to a target system specified a priori. Existence conditions for such schemes are established for various families of systems. The single-input and then the multi-input case relying on the controllability indices of the plants are first considered followed by an LMI approach combined with LMI regions for pole clustering. Then, the two original top-down and bottom-up methods are adapted to our framework and the stability problem for networks of non-identical dynamical agents is solved. The applicability of our approach for distributed network control is illustrated via a simple example.

Publication Type: Conference or Workshop Item (Paper)
Additional Information: © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Publisher Keywords: Stability criteria, Power system stability, Controllability, Decentralized control, Upper bound, Network topology
Departments: School of Science & Technology > Engineering
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