Dr. Hatem Elaydi Islamic University of Gaza EE Department Spring 2012 Lecture 3 Optimal Quadratic Control Variational Calculus & Continuous Optimal Control

Dynamic Optimization without Constraints Euler-Lagrange equations Associated transversality conditions Admissible trajectory 2

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Transversality Conditions 11

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Sufficient Conditions for (Weak) Extrema 15

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Unspecified Terminal time problem 23

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3.5 Euler-Lagrange equations & Transversality conditions-vector case 32

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3.6 A variational approach 37

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3.7 Dynamic optimization with equality constraints-Lagrange multipliers 40

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3.8 Dynamic optimization with inequality constraints 49

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Homework

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