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Nonlinear control synthesis by convex optimization

Prajna, Stephen and Parrilo, Pablo A. and Rantzer, Anders (2004) Nonlinear control synthesis by convex optimization. IEEE Transactions on Automatic Control, 49 (2). pp. 310-314. ISSN 0018-9286.

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A stability criterion for nonlinear systems, recently derived by the third author, can be viewed as a dual to Lyapunov's second theorem. The criterion is stated in terms of a function which can be interpreted as the stationary density of a substance that is generated all over the state-space and flows along the system trajectories toward the equilibrium. The new criterion has a remarkable convexity property, which in this note is used for controller synthesis via convex optimization. Recent numerical methods for verification of positivity of multivariate polynomials based on sum of squares decompositions are used.

Item Type:Article
Additional Information:© Copyright 2006 IEEE. Reprinted with permission Manuscript received November 6, 2002; revised August 29, 2003. [2004-02-19] Recommended by Associate Editor W. Kang. This work was supported by an exchange grant from the Swedish Foundation for International Cooperation in Research and Higher Education. The work of A. Rantzer was supported by the Swedish Research Council.
Subject Keywords:Density functions, nonlinear control, semidefinite programming relaxation, sum of squares decomposition
Record Number:CaltechAUTHORS:PRAieeetac04
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3186
Deposited By: Archive Administrator
Deposited On:19 May 2006
Last Modified:15 Jan 2015 20:41

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