Computational Optimal Control Tools and Practice
by Subchan, Subchan; Zbikowski, RafalEdition: 1st
Format: Hardcover
Pub. Date: 2009-08-17
Publisher(s): Wiley
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Summary
Computational Optimal Control: Tools and Practice provides a detailed guide to informed use of computational optimal control in advanced engineering practice, addressing the need for a better understanding of the practical application of optimal control using computational techniques.Throughout the text the authors employ an advanced aeronautical case study to provide a practical, real-life setting for optimal control theory. This case study focuses on an advanced, real-world problem known as the "terminal bunt manoeuvre" or special trajectory shaping of a cruise missile. Representing the many problems involved in flight dynamics, practical control and flight path constraints, this case study offers an excellent illustration of advanced engineering practice using optimal solutions. The book describes in practical detail the real and tested optimal control software, examining the advantages and limitations of the technology.Featuring tutorial insights into computational optimal formulations and an advanced case-study approach to the topic, Computational Optimal Control: Tools and Practice provides an essential handbook for practising engineers and academics interested in practical optimal solutions in engineering. Focuses on an advanced, real-world aeronautical case study examining optimisation of the bunt manoeuvre Covers DIRCOL, NUDOCCCS, PROMIS and SOCS (under the GESOP environment), and BNDSCO Explains how to configure and optimize software to solve complex real-world computational optimal control problems Presents a tutorial three-stage hybrid approach to solving optimal control problem formulations
Author Biography
Dr S Subchan, Cranfield University, UK
Dr Subchan is a research officer in the Department of Aerospace, Power and Sensors at Cranfield University's Shrivenham campus. He studied for his PhD at Cranfield in 2005, having previously worked for 3 years for Indonesian Aircraft Industries at Bandung on computational fluid dynamics.
Dr Rafal Zbikowski, Cranfield University, UK
Dr Zbikowski is Reader in Control Engineering and is a Principal Research Officer in the Guidance and Control Group of the Department of Aerospace, Power and Sensors at Cranfield University's Shrivenham campus. Prior to this he was a Post-Doctoral Research Fellow at Glasgow University leading the Glasgow side of a joint project with Daimler-Benz on neural adaptive control technology for Mercedes products. Dr Zbikowski has published over fifty papers on adaptive and nonlinear aspects of intelligent control, and flapping wing micro air vehicles. A control engineer with a strong mathematical background, he is a member of the American Mathematical Society (AMS) and the Institute of Electrical and Electronics Engineers (IEEE). Since 1998 he has been instrumental in obtaining UK funding for four substantial projects in the area of guidance and control.
Table of Contents
| Preface | p. ix |
| Acknowledgements xv | |
| Nomenclature | p. xvii |
| Introduction | p. 1 |
| Historical Context of Computational Optimal Control | p. 2 |
| Problem Formulation | p. 4 |
| Outline of the Book | p. 6 |
| Optimal Control: Outline of the Theory and Computation | p. 9 |
| Optimisation: From Finite to Infinite Dimension | p. 9 |
| Finite Dimension: Single Variable | p. 10 |
| Finite Dimension: Two or More Variables | p. 15 |
| Infinite Dimension | p. 24 |
| The Optimal Control Problem | p. 27 |
| Variational Approach to Problem Solution | p. 29 |
| Control Constraints | p. 32 |
| Mixed State-Control Inequality Constraints | p. 33 |
| State Inequality Constraints | p. 33 |
| Nonlinear Programming Approach to Solution | p. 34 |
| Numerical Solution of the Optimal Control Problem | p. 36 |
| Direct Method Approach | p. 36 |
| Indirect Method Approach | p. 43 |
| Summary and Discussion | p. 47 |
| Minimum Altitude Formulation | p. 49 |
| Minimum Altitude Problem | p. 49 |
| Qualitative Analysis | p. 50 |
| First Arc (Level Flight): Minimum Altitude Flight t0 <$> t <$> t1 | p. 50 |
| Second Arc: Climbing | p. 63 |
| Third Arc: Diving (t3 <$> t <$> tf) | p. 64 |
| Mathematical Analysis | p. 64 |
| The Problem with the Thrust Constraint Only | p. 64 |
| Optimal Control with Path Constraints | p. 66 |
| First Arc: Minimum Altitude Flight | p. 67 |
| Second Arc: Climbing | p. 69 |
| Third Arc: Diving | p. 70 |
| Indirect Method Solution | p. 71 |
| Co-state Approximation | p. 71 |
| Switching and Jump Conditions | p. 74 |
| Numerical Solution | p. 79 |
| Summary and Discussion | p. 80 |
| Comments on Switching Structure | p. 85 |
| Minimum Time Formulation | p. 95 |
| Minimum Time Problem | p. 96 |
| Qualitative Analysis | p. 96 |
| First Arc (Level Flight): Minimum Altitude Flight | p. 96 |
| Second Arc (Climbing) | p. 100 |
| Third Arc (Diving) | p. 100 |
| Mathematical Analysis | p. 101 |
| The Problem with the Thrust Constraint Only | p. 101 |
| Optimal Control with Path Constraints | p. 103 |
| First Arc: Minimum Altitude Flight | p. 104 |
| Second Arc: Climbing | p. 105 |
| Third Arc: Diving | p. 106 |
| Indirect Method Solutions | p. 107 |
| Summary and Discussion | p. 113 |
| Comments on Switching Structure | p. 113 |
| Software Implementation | p. 119 |
| DIRCOL implementation | p. 123 |
| User.f | p. 123 |
| Input File DATLIM | p. 128 |
| Input File DATDIM | p. 129 |
| Grid Refinement and Maximum Dimensions in DIRCOL | p. 132 |
| NUDOCCCS Implementation | p. 132 |
| Main Program | p. 133 |
| Subroutine MINFKT | p. 136 |
| Subroutine INTEGRAL | p. 136 |
| Subroutine DGLSYS | p. 136 |
| Subroutine ANFANGSW | p. 137 |
| Subroutine RANDBED | p. 138 |
| Subroutine NEBENBED | p. 138 |
| Subroutine CONBOXES | p. 139 |
| GESOP (PROMIS/SOCS) Implementation | p. 139 |
| Dynamic Equations, Subroutine fmrhs.f | p. 141 |
| Boundary Conditions, Subroutine fmbcon.f | p. 143 |
| Constraints, Subroutine fmpcon.f | p. 144 |
| Objective Function, Subroutine fmpcst.f | p. 145 |
| BNDSCO Implementation | p. 146 |
| Possible Sources of Error | p. 146 |
| BNDSCO Code | p. 148 |
| User Experience | p. 154 |
| Conclusions and Recommendations | p. 159 |
| Three-stage Manual Hybrid Approach | p. 159 |
| Generating an Initial Guess: Homotopy | p. 160 |
| Pure State Constraint and Multi-objective Formulation | p. 161 |
| Final Remarks | p. 162 |
| BNDSCO Benchmark Example | p. 165 |
| Analytic Solution | p. 165 |
| Unconstrained or Free Arc (l <$> 1/4) | p. 167 |
| Touch Point Case (1/6 <$> l <$> 1/4) | p. 168 |
| Constrained Arc Case (0 <$> l <$> 1/6) | p. 169 |
| Bibliography | p. 173 |
| Index | p. 179 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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