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Dr. Hatem Elaydi Islamic University of Gaza EE Department Spring 2012 Lecture 5 The Maximum Principle and Hamilton-Jacobi Theory Optimal Control.

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Presentation on theme: "Dr. Hatem Elaydi Islamic University of Gaza EE Department Spring 2012 Lecture 5 The Maximum Principle and Hamilton-Jacobi Theory Optimal Control."— Presentation transcript:

1 Dr. Hatem Elaydi Islamic University of Gaza EE Department Spring 2012 Lecture 5 The Maximum Principle and Hamilton-Jacobi Theory Optimal Control

2 4.1 Variational approach with terminal time not fixed 2 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

3 3

4 4

5 4.2 Weierstrass-Erdmann Conditions 5 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

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10 10 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

11 4.3 The Bolza Problem – No Inequality Constraints 11 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

12 4.3.1 Continuous optimal control problem – fixed beginning and terminal times – no inequality constraints 12 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

13 13 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

14 14 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

15 15 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

16 16 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

17 17 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

18 18 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

19 Example 4.3.1 19 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

20 20 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

21 21 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

22 4.3.2 COCP - fixed beginning & unspecified terminal times - no inequality constraints 22 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

23 23 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

24 24 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

25 25 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

26 26 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

27 27 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

28 28 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

29 4.4 The Bolza problem with inequality constraints Dr. H. Elaydi, EE Dept, IUG, Spring 2012 29 4.4.1 The maximum principle with control variable inequality constraints

30 30 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

31 31 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

32 32 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

33 33 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

34 34 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

35 35 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

36 36 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

37 37 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

38 38 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

39 39 Dr. H. Elaydi, EE Dept, IUG, Spring 2012

40 40 Dr. H. Elaydi, EE Dept, IUG, Spring 2012


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