Uncertainty-aware Integration of Control with Process Operations and Multi-parametric Programming Under Global Uncertainty

Supervisor’s Foreword......Page 7
Abstract......Page 9
Preface......Page 10
Parts of this thesis have been published in the following journal articles:......Page 12
Acknowledgements......Page 13
Contents......Page 14
List of Figures......Page 19
List of Tables......Page 24
List of Algorithms......Page 28
 1.1 Introduction and Research Questions......Page 29
 1.2 Thesis Scope and Outline......Page 33
Part I Theoretical and Algorithmic Advances  in Multi-parametric Programming Problems Under Global Uncertainty......Page 35
 2.1 Introduction......Page 36
 2.2 The Early Days of Parametric Optimisation: 1952--1967......Page 37
  2.3.1 From Parametric to Multi-parametric Linear Programming......Page 39
  2.3.2 From Sensitivity Analysis to Parametric Nonlinear Programming......Page 40
  2.3.3 Sensitivity Analysis and Parametric Integer Programming......Page 41
 2.4 Process Systems Engineering Led Multi-parametric Optimisation: 1993--Present......Page 43
  2.4.1 Multi-parametric (Mixed Integer) Linear Programming......Page 44
  2.4.2 Multi-parametric (Mixed Integer) Quadratic Programming......Page 46
  2.4.4 Multi-parametric (Mixed Integer) Nonlinear Programming......Page 49
  2.4.5 Convex Problems......Page 50
  2.4.7 Multi-parametric Dynamic Optimisation......Page 51
  2.5.1 Multi-parametric Multi-level Optimisation......Page 53
  2.5.2 Multi-parametric Model Predictive Control......Page 54
  2.5.3 Enterprise Wide Optimisation Under Uncertainty......Page 56
  2.5.5 Other Application Areas......Page 57
  2.6.1 Degeneracy Implications in mp-LPs/mp-QPs......Page 58
  2.6.2 Computational Complexity of mp-P Algorithms  and Reduction Strategies......Page 59
 2.7 Software Implementations......Page 61
 2.8 Conclusions—Quo vandis?......Page 62
 References......Page 63
 3.1 Introduction......Page 73
  3.2.1 A Computer Algebra Inspired Algorithm......Page 75
  3.2.2 Cylindrical Algebraic Decomposition and Comparison Procedure for Overlapping CRs......Page 77
 3.3 Global Uncertainty in General mp-MILPs......Page 88
 3.4 Computational Studies......Page 90
  3.4.1 Parametric Linear Program with LHS Unbounded Parameter......Page 91
  3.4.2 Discontinuous Mp-LP with LHS Uncertainty......Page 94
  3.4.3 Mp-LP Under Global Uncertainty......Page 98
  3.4.4 Mp-MILP Under Global Uncertainty......Page 101
  3.4.5 Case Study 1: Process Synthesis Under Global Uncertainty......Page 102
  3.4.6 Case Study 2: Process Scheduling Under Global Uncertainty......Page 105
 3.5 Discussion......Page 109
  3.5.1 Scalability of the Proposed Algorithm......Page 110
  3.5.2 Non-convexity of the Underlying Problem......Page 111
 References......Page 112
 4.1 Introduction......Page 115
  4.2.1 Multi-setpoint Explicit Controllers via Multi-parametric Programming......Page 118
  4.2.2 An Algorithm for the Global Solution of mp-NLPs......Page 121
  4.2.3 Motivating Example......Page 122
  4.3.1 Single-Input Single-Output Isothermal CSTR......Page 128
  4.3.2 Methyl-Methacrylate Polymerisation Isothermal CSTR......Page 132
  4.3.3 Overall Scalability of the Algorithm......Page 140
 4.4 Concluding Remarks......Page 141
 References......Page 144
Part II Uncertainty-Aware Integration of Planning, Scheduling and Control......Page 146
 5.1 Introduction......Page 147
  5.1.1 Integration of Process Operations with Control......Page 148
  5.1.2 Motivation and Problem Statement......Page 151
  5.2.1 Objective of the iPSC......Page 152
  5.2.2 Modelling the Planning and Scheduling Problem......Page 154
  5.2.3 Dynamic Optimisation (DO)......Page 158
  5.2.4 Linking Variables Between DO, Scheduling and Planning Model......Page 159
  5.2.5 Linking Equations Between DO and TSP Planning  and Scheduling......Page 161
  5.2.6 Monolithic and Decomposed Integration of Planning, Scheduling and optimal Control......Page 162
 5.3 Case Studies......Page 166
  5.3.1 SISO Multi-product CSTR......Page 167
  5.3.2 MIMO Multi-product CSTR......Page 173
  5.3.3 MMA Polymerisation Process......Page 177
 5.4 Concluding Remarks......Page 179
 References......Page 181
 6.1 Introduction......Page 183
 6.2 Literature Review......Page 185
 6.3 Mathematical Formulations......Page 186
  6.3.1 Modelling the Closed-Loop Integrated Planning, Scheduling and Control......Page 187
  6.3.2 The Overall Closed-Loop Integrated Framework......Page 189
 6.4 Case Studies......Page 194
  6.4.1 Single Input Single Output CSTR......Page 195
  6.4.2 MMA Polymerisation Reactor......Page 199
 References......Page 206
 7.1 Introduction and Motivation......Page 208
 7.2 Modelling and Optimisation with Uncertainty Considerations......Page 210
  7.2.1 Robust Optimisation......Page 211
  7.2.2 Stochastic Programming......Page 212
  7.2.3 Chance Constrained Programming......Page 213
  7.3.1 Rolling Horizon Strategy......Page 214
  7.3.2 Robust Optimisation for Process Planning......Page 217
  7.3.3 Chance-Constrained Process Scheduling......Page 220
  7.3.4 Overall Uncertainty-Aware iPSC Model......Page 222
  7.4.1 Problem Instance Classes and Tuning of the Proactive Module......Page 223
  7.4.2 Monte Carlo Simulations for Evaluation of the Proactive Module of the Uncertainty-Aware iPSC......Page 224
  7.5.1 Solution Quality of the Rolling Horizon Approach......Page 225
  7.5.2 Problem Class 1......Page 227
  7.5.3 Problem Class 2......Page 231
  7.5.4 Uncertainty Aware iPSC of MMA Polymerisation Process......Page 233
 References......Page 237
  8.1.1 Contributions......Page 241
  8.1.2 Perspectives for Future Research......Page 242
  8.2.1 Contributions......Page 243
  8.2.2 Perspectives for Future Research......Page 244
 References......Page 245
A.1.1  Algebraic Rings, Fields and Closures......Page 246
A.1.2  Polynomials, Ideals and Varieties......Page 247
A.2  Gröbner Bases......Page 249
A.2.2  Gröbner Bases Computation......Page 250
A.3.1  Semi-algebraic Sets and Quantified Formulas......Page 251
A.3.2  Cylindrical Algebraic Decomposition......Page 252
A.3.3  Basic Notions of Cylindrical Algebraic Decomposition......Page 253
A.3.4  Computation of the CAD......Page 254
B.1  Perseus: Parametric Algorithms for Explicit Optimisation of Resilient Systems Engineering Under Stochasticities......Page 258
B.2.3  Macaulay2......Page 259
B.2.6  Maple......Page 260
B.2.9  Singular......Page 261
B.3.1  Modelling of the mp-P Problem......Page 262
B.3.2  Solution of the mp-P Problem......Page 263
B.3.4  The Graphical User Interface (GUI)......Page 264
B.3.5  Ongoing Developments and Future Work......Page 265
Appendix C Multi-parametric Linear and Mixed Integer Linear Programming Under Global Uncertainty: Further Results......Page 268
Appendix D Open-Loop Integration of Planning, Scheduling and Optimal Control: Further Results......Page 275
Appendix E Detailed iPSC Model for the Rolling Horizon Solution Approach......Page 284