Stabilization of interconnected dynamical systems by online convex optimization

Hermans, Ralph M. and Lazar, Mircea and Jokić, Andrej (2014) Stabilization of interconnected dynamical systems by online convex optimization. = Stabilization of interconnected dynamical systems by online convex optimization. International Journal of Robust and Nonlinear Control, 24 (10). pp. 1467-1487. ISSN 1049-8923. Vrsta rada: ["eprint_fieldopt_article_type_article" not defined]. Kvartili JCR: Q1 (2013). Točan broj autora: 3.

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The problem of stabilizing networks of interconnected dynamical systems (NDS) in a scalable fashion is considered. As the first contribution, a generalized lemma and example network are provided to demonstrate that state-of-the-art, tractable dissipation-based NDS stabilization methods can fail even for simple unconstrained, linear, and time-invariant dynamics. Then, a solution to this issue is proposed, in which controller synthesis is decentralized via a set of parameterized storage functions. The corresponding stability conditions allow for max-type construction of a trajectory-specific Lyapunov function for the full closed-loop network, whereas neither of the local storage functions is required to be monotonically converging. The provided approach is indicated to be nonconservative in the sense that it can generate converging closed-loop trajectories for the motivating example network and a prescribed set of initial conditions. For input-affine NDS and quadratic parameterized storage functions, the synthesis scheme can be formulated as a set of low-complexity semidefinite programs that are solved online, in a receding horizon fashion. Moreover, for linear and time-invariant networks, an even simpler, explicit control scheme is derived by interpolating a collection of a priori generated converging state and control trajectories in a distributed fashion.

Item Type: Article (["eprint_fieldopt_article_type_article" not defined])
Keywords (Croatian): convex optimization; dynamical systems; large scale systems; Lyapunov functions; Lyapunov methods; trajectories; closed-loop networks; control trajectory; controller synthesis; distributed control; online convex optimizations; semidefinite programs; stability condition; stabilization methods; complex networks
Subjects: TECHNICAL SCIENCE > Basic technical sciences
Divisions: 900 Department of Robotics and Production System Automation > 910 Chair of Engineering Automation
Indexed in Web of Science: Yes
Indexed in Current Contents: Yes
Quartiles: Q1 (2013)
Date Deposited: 03 Jun 2015 06:46
Last Modified: 21 Nov 2018 11:26

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