Hamzi - Eurandom

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$Continuous-time random walks, fractional calculus and ... - Eurandom$

Experiment Control Input u(t) Outputs y(t) and ˆy(t) 1 0.5 0 −0.5 Control Input −1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (s) Original and Reduced System Responses 0.5 Original Reduced 0 −0.5 0 0.2 0.4 0.6 0.8 1 Time (s) 1.2 1.4 1.6 1.8 2 . . . . . . Boumediene <strong>Hamzi</strong> (Imperial College) On Control and RDS in RKHS June 4th, 2012 38 / 55
Experiment diag(TKcT T ) 10 −1 10 −2 10 −3 10 −4 10 −5 10 −6 Sorted Hankel Singular Values 10 1 2 3 4 5 6 7 −7 Index . . . . . . Boumediene <strong>Hamzi</strong> (Imperial College) On Control and RDS in RKHS June 4th, 2012 39 / 55
Page 1 and 2: Preliminary Results on Control and
Page 3 and 4: Outline • Review of Some Concepts
Page 5 and 6: Review of Some Concepts for Linear
Page 11 and 12: Controllability and Observability E
Page 13 and 14: Balancing of Linear Control Systems
Page 15 and 16: Balancing of Nonlinear Systems •
Page 17 and 18: Empirical Estimates of the Gramians
Page 19 and 20: Reproducing Kernel Hilbert Spaces
Page 21 and 22: Reproducing Kernel Hilbert Spaces T
Page 33 and 34: Balanced Reduction of Nonlinear Con
Page 35 and 36: Balancing in RKHS • “Balancing
Page 37: Experiment: Inputs ◮ Excite with
Page 45 and 46: Nonlinear SDEs in RKHSes • Assump
Page 47 and 48: Nonlinear SDEs in RKHSes • The st
Page 49 and 50: Parameter Estimation for SDEs • I
Page 51 and 52: Parameter Estimation for SDEs • I
Page 53 and 54: Example (A Fokker-Planck Integrable
Page 55: Open Questions • Derivation of da

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