Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
Structured adaptive control for solving LMIs. / Luzi, Alexandru Razvan; Fradkov, Alexander L.; Biannic, Jean Marc; Peaucelle, Dimitri.
11th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing, ALCOSP 2013 - Proceedings. PART. ed. International Federation of Automatic Control, 2013. p. 426-431 (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 11, No. PART).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
}
TY - GEN
T1 - Structured adaptive control for solving LMIs
AU - Luzi, Alexandru Razvan
AU - Fradkov, Alexander L.
AU - Biannic, Jean Marc
AU - Peaucelle, Dimitri
N1 - Funding Information: ★ This work was supported in part by the French Space Agency CNES and by part by Ministry of Education and Science of Russian Federation, the Federal Program ”Cadres” (agreements 8846, 8855).
PY - 2013
Y1 - 2013
N2 - 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 H1 norm computation problem. Solutions to the LMIs are obtained by simulations in Simulink.
AB - 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 H1 norm computation problem. Solutions to the LMIs are obtained by simulations in Simulink.
UR - http://www.scopus.com/inward/record.url?scp=84885694425&partnerID=8YFLogxK
U2 - 10.3182/20130703-3-FR-4038.00075
DO - 10.3182/20130703-3-FR-4038.00075
M3 - Conference contribution
AN - SCOPUS:84885694425
SN - 9783902823373
T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)
SP - 426
EP - 431
BT - 11th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing, ALCOSP 2013 - Proceedings
PB - International Federation of Automatic Control
T2 - 11th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing, ALCOSP 2013
Y2 - 3 July 2013 through 5 July 2013
ER -
ID: 87374791