1. Continuous Optimization

2. Copyright by Yu-Chi Ho2 First and second N.A.S.C. F Unconstraint optimization problem F Performance index: F Decision vector: F For a local minimum –Necessary conditions: u Stationary point –Sufficient conditions: u Positive semi-definite

3. Copyright by Yu-Chi Ho3 Constraints & LaGrange Multipliers F Constraints: F Problem: F Constraints: F State vector: F Unconstraint problem:

4. Copyright by Yu-Chi Ho4 Constraints & LaGrange Multipliers (contd.) F Constraints: F Unconstraint problem:

5. Copyright by Yu-Chi Ho5 A Big Picture Optimal ControlDecision Analysis LQG Special Cases LQ: Calculus of Variation Approach vs. Dynamic ProgrammingDynamic Programming G: Different System Dynamics Static State Dynamic State Under Control Current State (Estimation) Kalman Filter Bayes Rule Special Cases