Stochastic Modelling and Control

Häftad, Engelska, 2012

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The type of system we are interested in is a discrete-time or sampled-data system where the relation between input and output is (at least approximately) linear and where additive random dis turbances are also present, so that the behaviour of the system must be investigated by statistical methods.

Produktinformation

Utgivningsdatum2012-02-13
Mått140 x 216 x 21 mm
Vikt472 g
FormatHäftad
SpråkEngelska
SerieMonographs on Statistics and Applied Probability
Antal sidor394
FörlagSpringer
ISBN9789401086400

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1 Probability and linear system theory.- 1.1 Probability and random processes.- 1.2 Linear system theory.- Notes and references.- 2 Stochastic models.- 2.1 A general output process.- 2.2 Stochastic difference equations.- 2.3 ARMA noise models.- 2.4 Stochastic dynamical models.- 2.5 Innovations representations.- 2.6 Predictor models.- Notes and references.- 3 Filtering theory.- 3.1 The geometry of linear estimation.- 3.2 Recursive estimation.- 3.3 The Kalman filter.- 3.4 Innovations representation of state-space models.- Notes and references.- 4 System identification.- 4.1 Point estimation theory.- 4.2 Models.- 4.3 Parameter estimation for static systems.- 4.4 Parameter estimation for dynamical systems.- 4.5 Off-line identification algorithms.- 4.6 Algorithms for on-line parameter estimation.- 4.7 Bias arising from correlated disturbances.- 4.8 Three-stage least squares and order determination for scalar ARMAX models.- Notes and references.- 5 Asymptotic analysis of prediction error identification methods.- 5.1 Preliminary concepts and definitions.- 5.2 Asymptotic properties of the parameter estimates.- 5.3 Consistency.- 5.4 Interpretation of identification in terms of systems approximation.- Notes and references.- 6 Optimal control for state-space models.- 6.1 The deterministic linear regulator.- 6.2 The stochastic linear regulator.- 6.3 Partial observations and the separation principle.- Notes and references.- 7 Minimum variance and self-tuning control.- 7.1 Regulation for systems with known parameters.- 7.2 Pole/zero shifting regulators.- 7.3 Self-tuning regulators.- 7.4 A self-tuning controller with guaranteed convergence.- Notes and references.- Appendix A A uniform convergence theorem and proof of Theorem 5.2.1.- Appendix B The algebraic Riccati equation.- AppendixC Proof of Theorem 7.4.2.- Appendix D Some properties of matrices.- Appendix E Some inequalities of Hölder type.- Author index.