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Structured adaptive control for solving LMIs

Abstract : Numerical problems such as finding eigenvalues, singular value decomposition, linear programming, are traditionally solved with algorithms that can be interpreted as discrete-time processes. One can also find in the literature continuous-time methods for these same problems where solutions are the equilibrium points to which converge stable differential equations. The paper exposes one such continuous-time method for solving linear matrix inequalities. The proposed differential equations are those of an adaptive control feedback loop on an LTI system. The adaptive law is passivity-based with additional structural constraints of two types. The first constraint imposes the gain to be block-diagonal at all times. It can be interpreted as a decentralized control structure. The second constraint is only required asymptotically. It for example reads as requiring the feedback gain to be symmetric when time goes to infinity. Point-wise global stability is proved with quadratic Lyapunov functions. Results are illustrated on LMIs related to an H ∞ norm computation problem. Solutions to the LMIs are obtained by simulations in Simulink.
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https://hal.laas.fr/hal-03311172
Contributor : Dimitri Peaucelle <>
Submitted on : Friday, July 30, 2021 - 6:01:40 PM
Last modification on : Wednesday, August 18, 2021 - 1:52:57 PM

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Alexandru-Razvan Luzi, Alexander Fradkov, Jean-Marc Biannic, Dimitri Peaucelle. Structured adaptive control for solving LMIs. 11th IFAC Workshop on Adaptation and Learning in Control and Signal Processing, Jul 2013, Caen, France. pp.426-431, ⟨10.3182/20130703-3-FR-4038.00075⟩. ⟨hal-03311172⟩

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