Calculus of Variations & Optimal Control

Title......Page 1
Preface......Page 2
Course description......Page 3
Contents......Page 4
1.2 Objects of study in control theory......Page 6
1.3 Questions in control theory......Page 8
1.4 Appendix: systems of differential equations and etA......Page 9
2.2 Examples of optimal control problems......Page 13
2.3 Functionals......Page 16
2.4 The general form of the basic optimal control problem......Page 17
3.1 Introduction......Page 19
3.2 The brachistochrone problem......Page 20
3.3 Calculus of variations versus extremum problems......Page 21
3.4 Calculus in function spaces and beyond......Page 22
3.5 The simplest variational problem. Euler-Lagrange equation......Page 28
3.6 Free boundary conditions......Page 35
3.7 Generalization......Page 37
4.1 The simplest optimal control problem......Page 39
4.2 The Hamiltonian and Pontryagin minimum principle......Page 42
4.3 Generalization to vector inputs and states......Page 44
4.4 Constraint on the state at final time. Controllability......Page 47
5.1 The optimality principle......Page 50
5.2 Bellman’s equation......Page 52
Bibliography......Page 57
Index......Page 58
2004 Mock examination......Page 60