Multi-parametric Optimization and Control
Recent developments in multi-parametric optimization and control Multi-Parametric Optimization and Control provides comprehensive coverage of recent methodological developments for optimal model-based control through parametric optimization. It also shares real-world research applications to support...
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| Hauptverfasser: | , , |
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Newark
Wiley
2020
John Wiley & Sons, Incorporated Wiley-Blackwell |
| Ausgabe: | 1 |
| Schriftenreihe: | Wiley Series in Operations Research and Management Science |
| Schlagworte: | |
| ISBN: | 9781119265191, 1119265193, 9781119265184, 1119265185 |
| Online-Zugang: | Volltext |
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Inhaltsangabe:
- Cover -- Title Page -- Copyright -- Contents -- Short Bios of the Authors -- Preface -- Chapter 1 Introduction -- 1.1 Concepts of Optimization -- 1.1.1 Convex Analysis -- 1.1.1.1 Properties of Convex Sets -- 1.1.1.2 Properties of Convex Functions -- 1.1.2 Optimality Conditions -- 1.1.2.1 Karush-Kuhn-Tucker Necessary Optimality Conditions -- 1.1.2.2 Karun-Kush-Tucker First‐Order Sufficient Optimality Conditions -- 1.1.3 Interpretation of Lagrange Multipliers -- 1.2 Concepts of Multi‐parametric Programming -- 1.2.1 Basic Sensitivity Theorem -- 1.3 Polytopes -- 1.3.1 Approaches for the Removal of Redundant Constraints -- 1.3.1.1 Lower‐Upper Bound Classification -- 1.3.1.2 Solution of Linear Programming Problem -- 1.3.2 Projections -- 1.3.3 Modeling of the Union of Polytopes -- 1.4 Organization of the Book -- References -- Part I Multi‐parametric Optimization -- Chapter 2 Multi‐parametric Linear Programming -- 2.1 Solution Properties -- 2.1.1 Local Properties -- 2.1.2 Global Properties -- 2.2 Degeneracy -- 2.2.1 Primal Degeneracy -- 2.2.2 Dual Degeneracy -- 2.2.3 Connections Between Degeneracy and Optimality Conditions -- 2.3 Critical Region Definition -- 2.4 An Example: Chicago to Topeka -- 2.4.1 The Deterministic Solution -- 2.4.2 Considering Demand Uncertainty -- 2.4.3 Interpretation of the Results -- 2.5 Literature Review -- References -- Chapter 3 Multi‐Parametric Quadratic Programming -- 3.1 Calculation of the Parametric Solution -- 3.1.1 Solution via the Basic Sensitivity Theorem -- 3.1.2 Solution via the Parametric Solution of the KKT Conditions -- 3.2 Solution Properties -- 3.2.1 Local Properties -- 3.2.2 Global Properties -- 3.2.3 Structural Analysis of the Parametric Solution -- 3.3 Chicago to Topeka with Quadratic Distance Cost -- 3.3.1 Interpretation of the Results -- 3.4 Literature Review -- References
- Chapter 4 Solution Strategies for mp‐LP and mp‐QP Problems -- 4.1 General Overview -- 4.2 The Geometrical Approach -- 4.2.1 Define A Starting Point θ0 -- 4.2.2 Fix θ0 in Problem (4.1), and Solve the Resulting QP -- 4.2.3 Identify The Active Set for The Solution of The QP Problem -- 4.2.4 Move Outside the Found Critical Region and Explore the Parameter Space -- 4.3 The Combinatorial Approach -- 4.3.1 Pruning Criterion -- 4.4 The Connected‐Graph Approach -- 4.5 Discussion -- 4.6 Literature Review -- References -- Chapter 5 Multi‐parametric Mixed‐integer Linear Programming -- 5.1 Solution Properties -- 5.1.1 From mp‐LP to mp‐MILP Problems -- 5.1.2 The Properties -- 5.2 Comparing the Solutions from Different mp‐LP Problems -- 5.2.1 Identification of Overlapping Critical Regions -- 5.2.2 Performing the Comparison -- 5.2.3 Constraint Reversal for Coverage of Parameter Space -- 5.3 Multi‐parametric Integer Linear Programming -- 5.4 Chicago to Topeka Featuring a Purchase Decision -- 5.4.1 Interpretation of the Results -- 5.5 Literature Review -- References -- Chapter 6 Multi‐parametric Mixed‐integer Quadratic Programming -- 6.1 Solution Properties -- 6.1.1 From mp‐QP to mp‐MIQP Problems -- 6.1.2 The Properties -- 6.2 Comparing the Solutions from Different mp‐QP Problems -- 6.2.1 Identification of overlapping critical regions -- 6.2.2 Performing the Comparison -- 6.3 Envelope of Solutions -- 6.4 Chicago to Topeka Featuring Quadratic Cost and A Purchase Decision -- 6.4.1 Interpretation of the Results -- 6.5 Literature Review -- References -- Chapter 7 Solution Strategies for mp‐MILP and mp‐MIQP Problems -- 7.1 General Framework -- 7.2 Global Optimization -- 7.2.1 Introducing Suboptimality -- 7.3 Branch‐and‐Bound -- 7.4 Exhaustive Enumeration -- 7.5 The Comparison Procedure -- 7.5.1 Affine Comparison -- 7.5.2 Exact Comparison -- 7.6 Discussion
- 11.2 Disturbance Rejection -- 11.2.1 Explicit Disturbance Rejection - An Example of mp‐MPC -- 11.2.2 Results and Validation -- 11.3 Reference Trajectory Tracking -- 11.3.1 Reference Tracking to LQR Reformulation -- 11.3.2 Explicit Reference Tracking - An Example of mp‐MPC -- 11.3.3 Results and Validation -- 11.4 Moving Horizon Estimation -- 11.4.1 Multi‐parametric Moving Horizon Estimation -- 11.4.1.1 Current State -- 11.4.1.2 Recent Developments -- 11.4.1.3 Future Outlook -- 11.5 Other Developments in Explicit MPC -- References -- Chapter 12 PAROC: PARametric Optimization and Control -- 12.1 Introduction -- 12.2 The PAROC Framework -- 12.2.1 "High Fidelity" Modeling and Analysis -- 12.2.2 Model Approximation -- 12.2.2.1 Model Approximation Algorithms: A User Perspective Within the PAROC Framework -- 12.2.3 Multi‐parametric Programming -- 12.2.4 Multi‐parametric Moving Horizon Policies -- 12.2.5 Software Implementation and Closed‐Loop Validation -- 12.2.5.1 Multi‐parametric Programming Software -- 12.2.5.2 Integration of PAROC in gPROMS® ModelBuilder -- 12.3 Case Study: Distillation Column -- 12.3.1 "High Fidelity" Modeling -- 12.3.2 Model Approximation -- 12.3.3 Multi‐parametric Programming, Control, and Estimation -- 12.3.4 Closed‐Loop Validation -- 12.3.5 Conclusion -- 12.4 Case Study: Simple Buffer Tank -- 12.5 The Tank Example -- 12.5.1 "High Fidelity" Dynamic Modeling -- 12.5.2 Model Approximation -- 12.5.3 Design of the Multi‐parametric Model Predictive Controller -- 12.5.4 Closed‐Loop Validation -- 12.5.5 Conclusion -- 12.6 Concluding Remarks -- References -- A Appendix for the mp‐MPC Chapter 10 -- B Appendix for the mp‐MPC Chapter 11 -- B.1 Matrices for the mp‐QP Problem Corresponding to the Example of Section 11.3.2 -- Index -- EULA
- 7.6.1 Integer Handling -- 7.6.2 Comparison Procedure -- 7.7 Literature Review -- References -- Chapter 8 Solving Multi‐parametric Programming Problems Using MATLAB® -- 8.1 An Overview over the Functionalities of POP -- 8.2 Problem Solution -- 8.2.1 Solution of mp‐QP Problems -- 8.2.2 Solution of mp‐MIQP Problems -- 8.2.3 Requirements and Validation -- 8.2.4 Handling of Equality Constraints -- 8.2.5 Solving Problem (7.2) -- 8.3 Problem Generation -- 8.4 Problem Library -- 8.4.1 Merits and Shortcomings of The Problem Library -- 8.5 Graphical User Interface (GUI) -- 8.6 Computational Performance for Test Sets -- 8.6.1 Continuous Problems -- 8.6.2 Mixed‐integer Problems -- 8.7 Discussion -- Acknowledgments -- References -- Chapter 9 Other Developments in Multi‐parametric Optimization -- 9.1 Multi‐parametric Nonlinear Programming -- 9.1.1 The Convex Case -- 9.1.2 The Non‐convex Case -- 9.2 Dynamic Programming via Multi‐parametric Programming -- 9.2.1 Direct and Indirect Approaches -- 9.3 Multi‐parametric Linear Complementarity Problem -- 9.4 Inverse Multi‐parametric Programming -- 9.5 Bilevel Programming Using Multi‐parametric Programming -- 9.6 Multi‐parametric Multi‐objective Optimization -- References -- Part II Multi‐parametric Model Predictive Control -- Chapter 10 Multi‐parametric/Explicit Model Predictive Control -- 10.1 Introduction -- 10.2 From Transfer Functions to Discrete Time State‐Space Models -- 10.3 From Discrete Time State‐Space Models to Multi‐parametric Programming -- 10.4 Explicit LQR - An Example of mp‐MPC -- 10.4.1 Problem Formulation and Solution -- 10.4.2 Results and Validation -- 10.5 Size of the Solution and Online Computational Effort -- References -- Chapter 11 Extensions to Other Classes of Problems -- 11.1 Hybrid Explicit MPC -- 11.1.1 Explicit Hybrid MPC - An Example of mp‐MPC -- 11.1.2 Results and Validation