TY - GEN

T1 - Passification based adaptive control under coordinate-parametric white noise disturbances

AU - Fradkov, A. L.

AU - Razuvaeva, I. V.

AU - Grigoriev, G. K.

N1 - Funding Information: This work was supported in part by the Russian Foundation for Basic Research, project no. 08-01-00775 and by Federal Program ”Cadres”, contract 02.740.11.5056.

PY - 2010

Y1 - 2010

N2 - In the paper the basics of passification based adaptive control theory for stochastic continuous-time systems are introduced. Conditions for the mean square dissipativity of adaptive stabilization systems for a linear plant under coordinate-parametric white noise disturbances are obtained. A linear adaptive regulator with adaptation algorithm designed by the passification approach is proposed. The number of plant inputs may differ from that of outputs. The proof is based on the construction of a quadratic stochastic Lyapunov function. (In the case of purely parametric perturbations, the obtained conditions are known to be necessary and sufficient for the existence of a Lyapunov function with these properties.) Ultimate mean square boundedness (Levinson dissipativity) conditions for the designed closed loop system are obtained; it is shown that, in some special cases, the dissipativity of the closed loop system is preserved under white noise perturbations of arbitrary intensity. Stochastic G-passivity for nonsquare systems is introduced and necessary and sufficient conditions for strict stochastic G-passifiability are formulated.

AB - In the paper the basics of passification based adaptive control theory for stochastic continuous-time systems are introduced. Conditions for the mean square dissipativity of adaptive stabilization systems for a linear plant under coordinate-parametric white noise disturbances are obtained. A linear adaptive regulator with adaptation algorithm designed by the passification approach is proposed. The number of plant inputs may differ from that of outputs. The proof is based on the construction of a quadratic stochastic Lyapunov function. (In the case of purely parametric perturbations, the obtained conditions are known to be necessary and sufficient for the existence of a Lyapunov function with these properties.) Ultimate mean square boundedness (Levinson dissipativity) conditions for the designed closed loop system are obtained; it is shown that, in some special cases, the dissipativity of the closed loop system is preserved under white noise perturbations of arbitrary intensity. Stochastic G-passivity for nonsquare systems is introduced and necessary and sufficient conditions for strict stochastic G-passifiability are formulated.

KW - Adaptive control

KW - Ito equations

KW - Passification

KW - Stochastic dissipativity

UR - http://www.scopus.com/inward/record.url?scp=80051758922&partnerID=8YFLogxK

U2 - 10.3182/20100901-3-IT-2016.00266

DO - 10.3182/20100901-3-IT-2016.00266

M3 - Conference contribution

AN - SCOPUS:80051758922

SN - 9783902661807

T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)

SP - 659

EP - 664

BT - 8th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2010

PB - International Federation of Automatic Control

ER -