Hamzi - Eurandom

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

Context Goal: Combining tools from the theories of Dynamical Systems and Learning in view of analyzing, predicting and controling nonlinear systems on the basis of data rather than models. Approach: View Reproducing Kernel Hilbert Spaces as “Linearizing Spaces”, i.e. Nonlinear Systems will be mapped into an RKHS where Linear Systems Theory will be applied. . . . . . . Boumediene <strong>Hamzi</strong> (Imperial College) On Control and RDS in RKHS June 4th, 2012 2 / 55
Outline • Review of Some Concepts for Linear Control Systems • Elements of Learning Theory • On Nonlinear Control Systems in RKHS • Application: Model Reduction of Nonlinear Control Systems in RKHS • Review of Some Concepts for Linear SDEs • On Nonlinear SDEs in RKHSes • Application: Estimation of the Stationary Solution of the Fokker-Planck Equation of nonlinear SDEs • Application: Parameter Estimation of SDEs in RKHSes . . . . . . Boumediene <strong>Hamzi</strong> (Imperial College) On Control and RDS in RKHS June 4th, 2012 3 / 55
Page 1: Preliminary Results on Control and
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 and 38: Experiment: Inputs ◮ Excite with
Page 39 and 40: Experiment diag(TKcT T ) 10 −1 10
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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Hamzi - Eurandom

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