Modelling and Control of Dynamic Systems Using Gaussian Process Models (eBook)

Juš Kocijan is a senior research fellow at the Department of Systems and Control, Jozef Stefan Institute, the leading Slovenian research institute in the field of natural sciences and engineering, and a Professor of Electrical Engineering at the University of Nova Gorica, Slovenia. His past experience in the field of control engineering includes teaching and research at the University of Ljubljana and visiting research and teaching posts at several European universities and research institutes. He has been active in applied research in automatic control through numerous domestic and international research grants and projects, in a considerable number of which he acted as project leader. His research interests include the modelling of dynamic systems with Gaussian process models, control based on Gaussian process models, multiple-model approaches to modelling and control, applied nonlinear control, Individual Channel Analysis and Design. His other experience includes: serving as one of the editors of the Engineering Applications of Artificial Intelligence journal and on the editorial boards of other research journals, serving as a member of IFAC Technical committee on Computational Intelligence in Control, actively participating as a member of numerous scientific-meeting international programme and organising committees. Prof. Kocijan is a member of various national and international professional societies in the field of automatic control, modelling and simulation.

Series Editors’ Foreword 6
Preface 8
Contents 11
Symbols and Notation 13
Acronyms 15
1 Introduction 17
1.1 Introduction to Gaussian-Process Regression 19
1.1.1 Preliminaries 19
1.1.2 Gaussian-Process Regression 23
1.2 Relevance 32
1.3 Outline of the Book 33
References 34
2 System Identification with GP Models 37
2.1 The Model Purpose 41
2.2 Obtaining Data---Design of the Experiment ƒ 42
2.3 Model Setup 44
2.3.1 Model Structure 44
2.3.2 Selection of Regressors 49
2.3.3 Covariance Functions 51
2.4 GP Model Selection 63
2.4.1 Bayesian Model Inference 64
2.4.2 Marginal Likelihood---Evidence Maximisation 66
2.4.3 Estimation and Model Structure 72
2.4.4 Selection of Mean Function 75
2.4.5 Asymptotic Properties of GP Models 77
2.5 Computational Implementation 78
2.5.1 Direct Implementation 78
2.5.2 Indirect Implementation 80
2.5.3 Evolving GP Models 86
2.6 Validation 91
2.7 Dynamic Model Simulation 96
2.7.1 Numerical Approximation 97
2.7.2 Analytical Approximation of Statistical Moments with a Taylor Expansion 97
2.7.3 Unscented Transformation 98
2.7.4 Analytical Approximation with Exact Matching of Statistical Moments 99
2.7.5 Propagation of Uncertainty 100
2.7.6 When to Use Uncertainty Propagation? 102
2.8 An Example of GP Model Identification 103
References 111
3 Incorporation of Prior Knowledge 119
3.1 Different Prior Knowledge and Its Incorporation 119
3.1.1 Changing Input--Output Data 120
3.1.2 Changing the Covariance Function 122
3.1.3 Combination with the Presumed Structure 122
3.2 Wiener and Hammerstein GP Models 123
3.2.1 GP Modelling Used in the Wiener Model 124
3.2.2 GP Modelling Used in the Hammerstein Model 129
3.3 Incorporation of Local Models 134
3.3.1 Local Models Incorporated into a GP Model 138
3.3.2 Fixed-Structure GP Model 148
References 159
4 Control with GP Models 163
4.1 Control with an Inverse Dynamics Model 166
4.2 Optimal Control 171
4.3 Model Predictive Control 174
4.4 Adaptive Control 202
4.5 Gain Scheduling 204
4.6 Model Identification Adaptive Control 209
4.7 Control Using Iterative Learning 214
References 219
5 Trends, Challenges and Research Opportunities 225
References 227
6 Case Studies 229
6.1 Gas--Liquid Separator Modelling and Control 230
6.2 Faulty Measurements Detection and Reconstruction in Urban Traffic 246
6.3 Prediction of Ozone Concentration in the Air 257
References 266
Appendix A Mathematical Preliminaries 269
Appendix B Predictions 273
Appendix C Matlab Code 278
Index 279