{"product_id":"multiparametric-optimization-and-control-9781119265184","title":"Multiparametric Optimization and Control","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eRecent developments in multi-parametric optimization and control\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eMulti-Parametric Optimization and Control\u003c\/i\u003e provides comprehensive coverage of recent methodological developments for optimal model-based control through parametric optimization. It also shares real-world research applications to support deeper understanding of the material.\u003c\/p\u003e \u003cp\u003eResearchers and practitioners can use the book as reference. It is also suitable as a primary or a supplementary textbook. Each chapter looks at the theories related to a topic along with a relevant case study. Topic complexity increases gradually as readers progress through the chapters. The first part of the book presents an overview of the state-of-the-art multi-parametric optimization theory and algorithms in multi-parametric programming. The second examines the connection between multi-parametric programming and model-predictive controlfrom the linear quadratic regulator over hybrid systems to periodic systems and rob\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eShort Bios of the Authors xvii\u003c\/p\u003e \u003cp\u003ePreface xxi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction \u003c\/b\u003e\u003cb\u003e1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Concepts of Optimization 1\u003c\/p\u003e \u003cp\u003e1.1.1 Convex Analysis 1\u003c\/p\u003e \u003cp\u003e1.1.1.1 Properties of Convex Sets 2\u003c\/p\u003e \u003cp\u003e1.1.1.2 Properties of Convex Functions 2\u003c\/p\u003e \u003cp\u003e1.1.2 Optimality Conditions 3\u003c\/p\u003e \u003cp\u003e1.1.2.1 Karush–Kuhn–Tucker Necessary Optimality Conditions 5\u003c\/p\u003e \u003cp\u003e1.1.2.2 Karun–Kush–Tucker First-Order Sufficient Optimality Conditions 5\u003c\/p\u003e \u003cp\u003e1.1.3 Interpretation of Lagrange Multipliers 6\u003c\/p\u003e \u003cp\u003e1.2 Concepts of Multi-parametric Programming 6\u003c\/p\u003e \u003cp\u003e1.2.1 Basic Sensitivity Theorem 6\u003c\/p\u003e \u003cp\u003e1.3 Polytopes 9\u003c\/p\u003e \u003cp\u003e1.3.1 Approaches for the Removal of Redundant Constraints 11\u003c\/p\u003e \u003cp\u003e1.3.1.1 Lower-Upper Bound Classification 12\u003c\/p\u003e \u003cp\u003e1.3.1.2 Solution of Linear Programming Problem 13\u003c\/p\u003e \u003cp\u003e1.3.2 Projections 13\u003c\/p\u003e \u003cp\u003e1.3.3 Modeling of the Union of Polytopes 14\u003c\/p\u003e \u003cp\u003e1.4 Organization of the Book 16\u003c\/p\u003e \u003cp\u003eReferences 16\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Multi-parametric Optimization \u003c\/b\u003e\u003cb\u003e19\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Multi-parametric Linear Programming \u003c\/b\u003e\u003cb\u003e21\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Solution Properties 22\u003c\/p\u003e \u003cp\u003e2.1.1 Local Properties 23\u003c\/p\u003e \u003cp\u003e2.1.2 Global Properties 25\u003c\/p\u003e \u003cp\u003e2.2 Degeneracy 28\u003c\/p\u003e \u003cp\u003e2.2.1 Primal Degeneracy 29\u003c\/p\u003e \u003cp\u003e2.2.2 Dual Degeneracy 30\u003c\/p\u003e \u003cp\u003e2.2.3 Connections Between Degeneracy and Optimality Conditions 31\u003c\/p\u003e \u003cp\u003e2.3 Critical Region Definition 32\u003c\/p\u003e \u003cp\u003e2.4 An Example: Chicago to Topeka 33\u003c\/p\u003e \u003cp\u003e2.4.1 The Deterministic Solution 34\u003c\/p\u003e \u003cp\u003e2.4.2 Considering Demand Uncertainty 35\u003c\/p\u003e \u003cp\u003e2.4.3 Interpretation of the Results 36\u003c\/p\u003e \u003cp\u003e2.5 Literature Review 38\u003c\/p\u003e \u003cp\u003eReferences 39\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Multi-Parametric Quadratic Programming \u003c\/b\u003e\u003cb\u003e45\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Calculation of the Parametric Solution 47\u003c\/p\u003e \u003cp\u003e3.1.1 Solution \u003ci\u003evia \u003c\/i\u003ethe Basic Sensitivity Theorem 47\u003c\/p\u003e \u003cp\u003e3.1.2 Solution \u003ci\u003evia \u003c\/i\u003ethe Parametric Solution of the KKT Conditions 48\u003c\/p\u003e \u003cp\u003e3.2 Solution Properties 49\u003c\/p\u003e \u003cp\u003e3.2.1 Local Properties 49\u003c\/p\u003e \u003cp\u003e3.2.2 Global Properties 50\u003c\/p\u003e \u003cp\u003e3.2.3 Structural Analysis of the Parametric Solution 52\u003c\/p\u003e \u003cp\u003e3.3 Chicago to Topeka with Quadratic Distance Cost 55\u003c\/p\u003e \u003cp\u003e3.3.1 Interpretation of the Results 56\u003c\/p\u003e \u003cp\u003e3.4 Literature Review 61\u003c\/p\u003e \u003cp\u003eReferences 63\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Solution Strategies for mp-LP and mp-QP Problems \u003c\/b\u003e\u003cb\u003e67\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 General Overview 68\u003c\/p\u003e \u003cp\u003e4.2 The Geometrical Approach 70\u003c\/p\u003e \u003cp\u003e4.2.1 Define A Starting Point \u003ci\u003e𝜃\u003c\/i\u003e\u003csub\u003e0\u003c\/sub\u003e 70\u003c\/p\u003e \u003cp\u003e4.2.2 Fix \u003ci\u003e𝜃\u003c\/i\u003e\u003csub\u003e0\u003c\/sub\u003e in Problem (4.1), and Solve the Resulting QP 71\u003c\/p\u003e \u003cp\u003e4.2.3 Identify The Active Set for The Solution of The QP Problem 72\u003c\/p\u003e \u003cp\u003e4.2.4 Move Outside the Found Critical Region and Explore the Parameter Space 72\u003c\/p\u003e \u003cp\u003e4.3 The Combinatorial Approach 75\u003c\/p\u003e \u003cp\u003e4.3.1 Pruning Criterion 76\u003c\/p\u003e \u003cp\u003e4.4 The Connected-Graph Approach 78\u003c\/p\u003e \u003cp\u003e4.5 Discussion 81\u003c\/p\u003e \u003cp\u003e4.6 Literature Review 83\u003c\/p\u003e \u003cp\u003eReferences 85\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Multi-parametric Mixed-integer Linear Programming \u003c\/b\u003e\u003cb\u003e89\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Solution Properties 90\u003c\/p\u003e \u003cp\u003e5.1.1 From mp-LP to mp-MILP Problems 90\u003c\/p\u003e \u003cp\u003e5.1.2 The Properties 91\u003c\/p\u003e \u003cp\u003e5.2 Comparing the Solutions from Different mp-LP Problems 92\u003c\/p\u003e \u003cp\u003e5.2.1 Identification of Overlapping Critical Regions 93\u003c\/p\u003e \u003cp\u003e5.2.2 Performing the Comparison 95\u003c\/p\u003e \u003cp\u003e5.2.3 Constraint Reversal for Coverage of Parameter Space 95\u003c\/p\u003e \u003cp\u003e5.3 Multi-parametric Integer Linear Programming 96\u003c\/p\u003e \u003cp\u003e5.4 Chicago to Topeka Featuring a Purchase Decision 99\u003c\/p\u003e \u003cp\u003e5.4.1 Interpretation of the Results 99\u003c\/p\u003e \u003cp\u003e5.5 Literature Review 102\u003c\/p\u003e \u003cp\u003eReferences 103\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Multi-parametric Mixed-integer Quadratic Programming \u003c\/b\u003e\u003cb\u003e107\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Solution Properties 109\u003c\/p\u003e \u003cp\u003e6.1.1 From mp-QP to mp-MIQP Problems 109\u003c\/p\u003e \u003cp\u003e6.1.2 The Properties 109\u003c\/p\u003e \u003cp\u003e6.2 Comparing the Solutions from Different mp-QP Problems 110\u003c\/p\u003e \u003cp\u003e6.2.1 Identification of overlapping critical regions 112\u003c\/p\u003e \u003cp\u003e6.2.2 Performing the Comparison 112\u003c\/p\u003e \u003cp\u003e6.3 Envelope of Solutions 113\u003c\/p\u003e \u003cp\u003e6.4 Chicago to Topeka Featuring Quadratic Cost and A Purchase Decision 114\u003c\/p\u003e \u003cp\u003e6.4.1 Interpretation of the Results 115\u003c\/p\u003e \u003cp\u003e6.5 Literature Review 119\u003c\/p\u003e \u003cp\u003eReferences 121\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Solution Strategies for mp-MILP and mp-MIQP Problems \u003c\/b\u003e\u003cb\u003e125\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 General Framework 126\u003c\/p\u003e \u003cp\u003e7.2 Global Optimization 127\u003c\/p\u003e \u003cp\u003e7.2.1 Introducing Suboptimality 129\u003c\/p\u003e \u003cp\u003e7.3 Branch-and-Bound 130\u003c\/p\u003e \u003cp\u003e7.4 Exhaustive Enumeration 133\u003c\/p\u003e \u003cp\u003e7.5 The Comparison Procedure 134\u003c\/p\u003e \u003cp\u003e7.5.1 Affine Comparison 135\u003c\/p\u003e \u003cp\u003e7.5.2 Exact Comparison 137\u003c\/p\u003e \u003cp\u003e7.6 Discussion 138\u003c\/p\u003e \u003cp\u003e7.6.1 Integer Handling 138\u003c\/p\u003e \u003cp\u003e7.6.2 Comparison Procedure 141\u003c\/p\u003e \u003cp\u003e7.7 Literature Review 142\u003c\/p\u003e \u003cp\u003eReferences 144\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Solving Multi-parametric Programming Problems Using MATLAB\u003csup\u003e®\u003c\/sup\u003e \u003c\/b\u003e\u003cb\u003e147\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 An Overview over the Functionalities of POP 148\u003c\/p\u003e \u003cp\u003e8.2 Problem Solution 148\u003c\/p\u003e \u003cp\u003e8.2.1 Solution of mp-QP Problems 148\u003c\/p\u003e \u003cp\u003e8.2.2 Solution of mp-MIQP Problems 148\u003c\/p\u003e \u003cp\u003e8.2.3 Requirements and Validation 149\u003c\/p\u003e \u003cp\u003e8.2.4 Handling of Equality Constraints 149\u003c\/p\u003e \u003cp\u003e8.2.5 Solving Problem (7.2) 149\u003c\/p\u003e \u003cp\u003e8.3 Problem Generation 150\u003c\/p\u003e \u003cp\u003e8.4 Problem Library 151\u003c\/p\u003e \u003cp\u003e8.4.1 Merits and Shortcomings of The Problem Library 152\u003c\/p\u003e \u003cp\u003e8.5 Graphical User Interface (GUI) 153\u003c\/p\u003e \u003cp\u003e8.6 Computational Performance for Test Sets 154\u003c\/p\u003e \u003cp\u003e8.6.1 Continuous Problems 154\u003c\/p\u003e \u003cp\u003e8.6.2 Mixed-integer Problems 154\u003c\/p\u003e \u003cp\u003e8.7 Discussion 156\u003c\/p\u003e \u003cp\u003eAcknowledgments 162\u003c\/p\u003e \u003cp\u003eReferences 162\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Other Developments in Multi-parametric Optimization \u003c\/b\u003e\u003cb\u003e165\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Multi-parametric Nonlinear Programming 165\u003c\/p\u003e \u003cp\u003e9.1.1 The Convex Case 166\u003c\/p\u003e \u003cp\u003e9.1.2 The Non-convex Case 167\u003c\/p\u003e \u003cp\u003e9.2 Dynamic Programming via Multi-parametric Programming 167\u003c\/p\u003e \u003cp\u003e9.2.1 Direct and Indirect Approaches 169\u003c\/p\u003e \u003cp\u003e9.3 Multi-parametric Linear Complementarity Problem 170\u003c\/p\u003e \u003cp\u003e9.4 Inverse Multi-parametric Programming 171\u003c\/p\u003e \u003cp\u003e9.5 Bilevel Programming Using Multi-parametric Programming 172\u003c\/p\u003e \u003cp\u003e9.6 Multi-parametric Multi-objective Optimization 173\u003c\/p\u003e \u003cp\u003eReferences 174\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Multi-parametric Model Predictive Control \u003c\/b\u003e\u003cb\u003e187\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Multi-parametric\/Explicit Model Predictive Control \u003c\/b\u003e\u003cb\u003e189\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 189\u003c\/p\u003e \u003cp\u003e10.2 From Transfer Functions to Discrete Time State-Space Models 191\u003c\/p\u003e \u003cp\u003e10.3 From Discrete Time State-Space Models to Multi-parametric Programming 195\u003c\/p\u003e \u003cp\u003e10.4 Explicit LQR – An Example of mp-MPC 200\u003c\/p\u003e \u003cp\u003e10.4.1 Problem Formulation and Solution 200\u003c\/p\u003e \u003cp\u003e10.4.2 Results and Validation 202\u003c\/p\u003e \u003cp\u003e10.5 Size of the Solution and Online Computational Effort 206\u003c\/p\u003e \u003cp\u003eReferences 207\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Extensions to Other Classes of Problems \u003c\/b\u003e\u003cb\u003e211\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Hybrid Explicit MPC 211\u003c\/p\u003e \u003cp\u003e11.1.1 Explicit Hybrid MPC – An Example of mp-MPC 213\u003c\/p\u003e \u003cp\u003e11.1.2 Results and Validation 215\u003c\/p\u003e \u003cp\u003e11.2 Disturbance Rejection 219\u003c\/p\u003e \u003cp\u003e11.2.1 Explicit Disturbance Rejection – An Example of mp-MPC 220\u003c\/p\u003e \u003cp\u003e11.2.2 Results and Validation 222\u003c\/p\u003e \u003cp\u003e11.3 Reference Trajectory Tracking 222\u003c\/p\u003e \u003cp\u003e11.3.1 Reference Tracking to LQR Reformulation 227\u003c\/p\u003e \u003cp\u003e11.3.2 Explicit Reference Tracking – An Example of mp-MPC 230\u003c\/p\u003e \u003cp\u003e11.3.3 Results and Validation 232\u003c\/p\u003e \u003cp\u003e11.4 Moving Horizon Estimation 232\u003c\/p\u003e \u003cp\u003e11.4.1 Multi-parametric Moving Horizon Estimation 232\u003c\/p\u003e \u003cp\u003e11.4.1.1 Current State 237\u003c\/p\u003e \u003cp\u003e11.4.1.2 Recent Developments 237\u003c\/p\u003e \u003cp\u003e11.4.1.3 Future Outlook 238\u003c\/p\u003e \u003cp\u003e11.5 Other Developments in Explicit MPC 239\u003c\/p\u003e \u003cp\u003eReferences 240\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 PAROC: PARametric Optimization and Control \u003c\/b\u003e\u003cb\u003e243\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 243\u003c\/p\u003e \u003cp\u003e12.2 The PAROC Framework 246\u003c\/p\u003e \u003cp\u003e12.2.1 “High Fidelity” Modeling and Analysis 247\u003c\/p\u003e \u003cp\u003e12.2.2 Model Approximation 247\u003c\/p\u003e \u003cp\u003e12.2.2.1 Model Approximation Algorithms: A User Perspective Within the PAROC Framework 247\u003c\/p\u003e \u003cp\u003e12.2.3 Multi-parametric Programming 257\u003c\/p\u003e \u003cp\u003e12.2.4 Multi-parametric Moving Horizon Policies 259\u003c\/p\u003e \u003cp\u003e12.2.5 Software Implementation and Closed-LoopValidation 259\u003c\/p\u003e \u003cp\u003e12.2.5.1 Multi-parametric Programming Software 259\u003c\/p\u003e \u003cp\u003e12.2.5.2 Integration of PAROC in gPROMS\u003csup\u003e®\u003c\/sup\u003e ModelBuilder 260\u003c\/p\u003e \u003cp\u003e12.3 Case Study: Distillation Column 261\u003c\/p\u003e \u003cp\u003e12.3.1 “High Fidelity” Modeling 262\u003c\/p\u003e \u003cp\u003e12.3.2 Model Approximation 264\u003c\/p\u003e \u003cp\u003e12.3.3 Multi-parametric Programming, Control, and Estimation 265\u003c\/p\u003e \u003cp\u003e12.3.4 Closed-Loop Validation 267\u003c\/p\u003e \u003cp\u003e12.3.5 Conclusion 268\u003c\/p\u003e \u003cp\u003e12.4 Case Study: Simple Buffer Tank 269\u003c\/p\u003e \u003cp\u003e12.5 The Tank Example 269\u003c\/p\u003e \u003cp\u003e12.5.1 “High Fidelity” Dynamic Modeling 269\u003c\/p\u003e \u003cp\u003e12.5.2 Model Approximation 270\u003c\/p\u003e \u003cp\u003e12.5.3 Design of the Multi-parametric Model Predictive Controller 271\u003c\/p\u003e \u003cp\u003e12.5.4 Closed-Loop Validation 272\u003c\/p\u003e \u003cp\u003e12.5.5 Conclusion 273\u003c\/p\u003e \u003cp\u003e12.6 Concluding Remarks 273\u003c\/p\u003e \u003cp\u003eReferences 273\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA Appendix for the mp-MPC Chapter 10 \u003c\/b\u003e\u003cb\u003e281\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eB Appendix for the mp-MPC Chapter 11 \u003c\/b\u003e\u003cb\u003e285\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB.1 Matrices for the mp-QP Problem Corresponding to the\u003c\/p\u003e \u003cp\u003eExample of Section 11.3.2 285\u003c\/p\u003e \u003cp\u003eIndex 291\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49407022891351,"sku":"9781119265184","price":98.06,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119265184.jpg?v=1730497908","url":"https:\/\/bookcurl.com\/products\/multiparametric-optimization-and-control-9781119265184","provider":"Book Curl","version":"1.0","type":"link"}