1 Preliminaries.- 1.1 Introduction.- 1.2 An example: flocculation model.- 1.3 The aim of the new development.- 1.

4 The structure of the book.- 1.5 Random variables and stochastic processes.- 1.5.1 Random variables and their distribution functions.- 1.5.

2 Mean and variance.- 1.5.3 Random vector.- 1.5.4 Conditional mean.- 1.

6 Stochastic processes.- 1.7 Some typical distributions.- 1.7.1 Gaussian distribution.- 1.7.

2 Uniform distribution.- 1.7.3 ? distribution.- 1.8 Conclusions.- 2 Control of SISO Stochastic Systems: A Fundamental Control Law.- 2.

1 Introduction.- 2.2 Preliminaries on B-splines artificial neural networks.- 2.3 Model representation.- 2.3.1 Static models.

- 2.3.2 Dynamic models.- 2.4 System modelling and parameter estimation.- 2.4.1 Modelling of static systems.

- 2.4.2 Modelling of linear dynamic systems.- 2.5 Control algorithm design.- 2.5.1 Control algorithm for static systems.

- 2.5.2 Control algorithm for linear dynamic systems.- 2.5.3 Constraints on input energy for dynamic systems.- 2.6 Discussions.

- 2.6.1 Adaptive control.- 2.6.2 Modelling and control of time delay systems.- 2.6.

3 On-line measurement of Vk.- 2.6.4 Controllability, observability and stability.- 2.7 Examples.- 2.7.

1 Static system modelling.- 2.7.2 A design example for dynamic systems.- 2.8 Conclusions.- 3 Control of MIMO Stochastic Systems: Robustness and Stability.- 3.

1 Introductionx.- 3.2 Model representation.- 3.2.1 State space form.- 3.2.

2 The input-output form.- 3.3 The controller using V(k).- 3.3.1 Measurement of V(k).- 3.3.

2 Feedback control using V(k).- 3.3.3 Stability issues.- 3.4 The controller using f(y, U(k)).- 3.4.

1 The formulation of control algorithm.- 3.4.2 Stability issues.- 3.5 An illustrative example.- 3.5.

1 Control algorithm design.- 3.5.2 Simulation results.- 3.6 Conclusions and discussions.- 4 Realization of Perfect Tracking.- 4.

1 Introduction.- 4.2 Preliminaries and model representation.- 4.3 Main result.- 4.4 Simulation results.- 4.

4.1 Controller design.- 4.4.2 Simulation results.- 4.5 An LQR based algorithm.- 4.

6 Conclusions.- 5 Stable Adaptive Control of Stochastic Distributions.- 5.1 Introduction.- 5.2 Model representation.- 5.3 On-line estimation and its convergence.

- 5.4 Adaptive control algorithm design.- 5.5 Stability analysis.- 5.6 A simulated example.- 5.7 Conclusions.

- 6 Model Reference Adaptive Control.- 6.1 Introduction.- 6.2 Model representation.- 6.3 An adaptive controller design.- 6.

3.1 Construction of the reference model.- 6.3.2 Construction of error dynamics.- 6.4 Adaptive tuning rules for K(t) and Q(t).- 6.

5 Robust adaptive control scheme.- 6.5.1 Control scheme when ?(t) ? 0.- 6.5.2 Control scheme when both e0 and ? are present.- 6.

6 A case study.- 6.7 Conclusions and discussions.- 7 Control of Nonlinear Stochastic Systems.- 7.1 Introduction.- 7.2 Model representation.

- 7.3 Control algorithm design.- 7.4 Stability issues.- 7.5 A neural network approach.- 7.5.

1 Training of the neural networks.- 7.5.2 A linearised control algorithm.- 7.6 Two examples.- 7.7 Calculation of ?.

- 7.8 Conclusions.- 8 Application to Fault Detection.- 8.1 Introduction.- 8.2 Model representation.- 8.

3 Fault detection.- 8.3.1 Fault detection for static systems.- 8.3.2 Dynamic systems.- 8.

3.3 Fault detection signal.- 8.4 An adaptive diagnostic observer.- 8.5 Discussions.- 8.6 An identification based FDD.

- 8.7 Fault diagnosis.- 8.7.1 The algorithm.- 8.7.2 An applicability study.

- 8.8 Discussions and conclusions.- 9 Advanced Topics.- 9.1 Introduction.- 9.2 Square root models.- 9.

3 Control algorithm design.- 9.3.1 Finding weights from ?(y, u(k)).- 9.3.2 The control algorithm.- 9.

4 Simulations.- 9.5 Continuous-time models.- 9.6 The control algorithm.- 9.7 Control of the mean and variance.- 9.

7.1 The control of output mean value.- 9.7.2 The control of output variance.- 9.8 Singular stochastic systems.- 9.

8.1 Model representation.- 9.8.2 Control algorithm design.- 9.9 Pseudo ARMAX systems.- 9.

10 Filtering issues.- 9.11 Conclusions.- References.