Technical University of Crete

1. INTRODUCTION

2.THE THEORY OF DISCRETE-TIME OPTIMAL CONTROL

2.1. Problem Formulation
2.2. Optimality Conditions
2.3. Extensions

3. FEASIBLE DIRECTION ALGORITHM

3.1. Reduced Gradient
3.2. Basic Algorithmic Structure
3.3. Specification of a Search Direction

3.3.1. Steepest Descent
3.3.2. Quasi-Newton Methods
3.3.3. Conjugate Gradient Methods

3.4. Line Optimization

3.4.1. The One-Dimensional Line Function
3.4.2. Numerical Line Search Algorithm

3.5. Convergence Test
3.6. Restart
3.7. Scaling
3.8. Examples

4. EXTENSIONS

4.1. Constant Control Bounds
4.2. State-Dependent Control Bounds
4.3. Linear Control Constraints

4.3.1. General Background
4.3.2. Calculation of Feasible Control Variables
4.3.3 Algorithmic Modifications

4.4 State-Dependent Linear Control Constraints
4.5 Further Extensions

5. CONCLUSIONS

REFERENCES

APPENDIX A: OPTIMALITY OF EXTENDED ALGORITHM

A.1. Constant Control Bounds
A.2 Linear Control Constraints