Stochastic Modelling and Control

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.- Appendix C Proof of Theorem 7.4.2.- Appendix D Some properties of matrices.- Appendix E Some inequalities of Holder type.- Author index.