Computational Optimal Control: Tools and Practice

Acknowledgements

Nomenclature

1 Introduction

1.1 Historical Context of Computational Optimal Control

1.2 Problem Formulation

1.3 Outline of the Book

2 Optimal Control: Outline of the Theory and Computation

2.1 Optimisation: From Finite to Infinite Dimension

2.2 The Optimal Control Problem

2.3 Variational Approach to Problem Solution

2.4 Nonlinear Programming Approach to Solution 

2.5 Numerical Solution of the Optimal Control Problem.

2.6 Summary and Discussion

3 Minimum Altitude Formulation

3.1 Minimum Altitude Problem

3.2 Qualitative Analysis

3.3 Mathematical Analysis

3.4 Indirect Method Solution

3.5 Summary and Discussion

4 Minimum Time Formulation

4.1 Minimum Time Problem

4.2 Qualitative Analysis

4.3 Mathematical Analysis

4.4 Indirect Method Solutions

4.5 Summary and Discussion

5 Software Implementation

5.1 DIRCOL implementation

5.2 NUDOCCCS Implementation

5.3 GESOP (PROMIS/SOCS) Implementation

5.4 BNDSCO Implementation

5.5 User Experience

6 Conclusions and Recommendations

6.1 Three-stage Manual Hybrid Approach

6.2 Generating an Initial Guess: Homotopy

6.3 Pure State Constraint and Multi-objective Formulation

6.4 Final Remarks

Appendix BNDSCO Benchmark Example

A.1 Analytic Solution

A.1.1 Unconstrained or Free Arc (l ≥1/4)

A.1.2 Touch Point Case (1/6 ≤l ≤1/4)

A.1.3 Constrained Arc Case (0 ≤l ≤1/6)

Bibliography

Index