Economic Model Predictive Control (eBook)

Dr. Liu received the BS and MS degrees in Control Science and Engineering from Zhejiang University in 2003 and 2006, respectively. He received the PhD degree in Chemical Engineering from the University of California, Los Angeles in 2011. Before joining the University of Alberta in April, 2012, Dr. Liu was a postdoctoral researcher at the University of California, Los Angeles. His research interests are in the general areas of process control theory and practice with emphasis on model predictive control, networked and distributed control, process monitoring, and real-time control of chemical processes and energy generation systems. Professor Panagiotis Christofides obtained his PhD from the University of Minnesota in 1996 and he has been a professor at the University of California, Los Angeles since 2004. He is a fellow of various professional societies:  the American Association for the Advancement of Science, the International Federation of Automatic Control and the IEEE. He is the author of numerous research papers, as well as two previous books published by Springer and has much experience of conference organization having served on various boards at various times, among them as the AIChE Director on the American Automatic Control Council. 

Series Editors’ Foreword 6
Preface 9
Contents 11
List of Figures 15
List of Tables 23
1 Introduction 25
1.1 Motivation 25
1.2 Tracking Versus Economic Model Predictive Control: A High-Level Overview 28
1.3 Chemical Processes and Time-Varying Operation 30
1.3.1 Catalytic Oxidation of Ethylene 31
1.3.2 Continuously-Stirred Tank Reactor with Second-Order Reaction 34
1.4 Objectives and Organization of the Book 39
References 41
2 Background on Nonlinear Systems, Control, and Optimization 44
2.1 Notation 44
2.2 Stability of Nonlinear Systems 45
2.2.1 Lyapunov's Direct Method 48
2.2.2 LaSalle's Invariance Principle 49
2.3 Stabilization of Nonlinear Systems 50
2.3.1 Control Lyapunov Functions 50
2.3.2 Stabilization of Nonlinear Sampled-Data Systems 52
2.3.3 Tracking Model Predictive Control 57
2.3.4 Tracking Lyapunov-Based MPC 59
2.4 Brief Review of Nonlinear and Dynamic Optimization 60
2.4.1 Notation 61
2.4.2 Definitions and Optimality Conditions 62
2.4.3 Nonlinear Optimization Solution Strategies 65
2.4.4 Dynamic Optimization 69
References 76
3 Brief Overview of EMPC Methods and Some Preliminary Results 79
3.1 Background on EMPC Methods 79
3.1.1 Class of Nonlinear Systems 79
3.1.2 EMPC Methods 81
3.2 Application of EMPC to a Chemical Process Example 89
References 93
4 Lyapunov-Based EMPC: Closed-Loop Stability, Robustness, and Performance 96
4.1 Introduction 96
4.2 Lyapunov-Based EMPC Design and Implementation 97
4.2.1 Class of Nonlinear Systems 97
4.2.2 Stabilizability Assumption 97
4.2.3 LEMPC Formulation 98
4.2.4 Implementation Strategy 101
4.2.5 Satisfying State Constraints 102
4.2.6 Extensions and Variants of LEMPC 104
4.3 Closed-Loop Stability and Robustness Under LEMPC 106
4.3.1 Synchronous Measurement Sampling 106
4.3.2 Asynchronous and Delayed Sampling 112
4.3.3 Application to a Chemical Process Example 117
4.4 Closed-Loop Performance Under LEMPC 125
4.4.1 Stabilizability Assumption 125
4.4.2 Formulation and Implementation of the LEMPC with a Terminal Equality Constraint 126
4.4.3 Closed-Loop Performance and Stability Analysis 127
4.5 LEMPC with a Time-Varying Stage Cost 133
4.5.1 Class of Economic Costs and Stabilizability Assumption 133
4.5.2 The Union of the Stability Regions 134
4.5.3 Formulation of LEMPC with Time-Varying Economic Cost 137
4.5.4 Implementation Strategy 139
4.5.5 Stability Analysis 140
4.5.6 Application to a Chemical Process Example 142
4.6 Conclusions 153
References 153
5 State Estimation and EMPC 155
5.1 Introduction 155
5.1.1 System Description 156
5.1.2 Stabilizability Assumption 156
5.2 High-Gain Observer-Based EMPC Scheme 157
5.2.1 State Estimation via High-Gain Observer 159
5.2.2 High-Gain Observer-Based EMPC 160
5.2.3 Closed-Loop Stability Analysis 162
5.2.4 Application to a Chemical Process Example 166
5.3 RMHE-Based EMPC Scheme 173
5.3.1 Observability Assumptions 174
5.3.2 Robust MHE 175
5.3.3 RMHE-Based EMPC 177
5.3.4 Stability Analysis 180
5.3.5 Application to a Chemical Process Example 185
5.4 Conclusions 189
References 189
6 Two-Layer EMPC Systems 191
6.1 Introduction 191
6.1.1 Notation 192
6.2 Two-Layer Control and Optimization Framework 194
6.2.1 Class of Systems 194
6.2.2 Formulation and Implementation 195
6.2.3 Application to a Chemical Process 205
6.3 Unifying Dynamic Optimization with Time-Varying Economics and Control 211
6.3.1 Stabilizability Assumption 212
6.3.2 Two-Layer EMPC Scheme Addressing Time-Varying Economics 213
6.3.3 Application to a Chemical Process Example 221
6.4 Addressing Closed-Loop Performance 228
6.4.1 Class of Systems 229
6.4.2 Stabilizability Assumption 230
6.4.3 Two-Layer EMPC Structure 231
6.4.4 Application to Chemical Process Example 240
6.5 Conclusions 250
References 251
7 EMPC Systems: Computational Efficiency and Real-Time Implementation 253
7.1 Introduction 253
7.2 Economic Model Predictive Control of Nonlinear Singularly Perturbed Systems 254
7.2.1 Class of Nonlinear Singularly Perturbed Systems 254
7.2.2 Two-Time-Scale Decomposition 255
7.2.3 Stabilizability Assumption 257
7.2.4 LEMPC of Nonlinear Singularly Perturbed Systems 258
7.2.5 Application to a Chemical Process Example 269
7.3 Distributed EMPC: Evaluation of Sequential and Iterative Architectures 272
7.3.1 Centralized EMPC 274
7.3.2 Sequential DEMPC 275
7.3.3 Iterative DEMPC 278
7.3.4 Evaluation of DEMPC Approaches 281
7.4 Real-Time Economic Model Predictive Control of Nonlinear Process Systems 282
7.4.1 Class of Systems 284
7.4.2 Real-Time LEMPC Formulation 285
7.4.3 Implementation Strategy 286
7.4.4 Stability Analysis 290
7.4.5 Application to a Chemical Process Network 295
7.5 Conclusions 307
References 308
Index 310