Bounded Dynamic Stochastic Systems: Modelling and Control

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.