• Introduction, definitions, reformulation of benchmark control theory problems as optimization problems
• Linear case, simplex method
• Monovariable optimization: Classical, and DFO (derivative-free optimization) methods; « economical » methods, notion of Mini-max problems
• Multivariable optimization: analytical/heuristical methods, exact and numerical solution of quadratic form like problems. Example of Limited-memory BFGS for neural networks
• Constrained optimization: examples of constraints in control. Reformulation of the constrained problem, primal and dual methods, definition and solution of the Lagrangian function
• Functional optimization: Euler-Lagrange equations, brachistochrone problem (optimal trajectory), isoperimetric optimization (Dido’s problem)
• Maximum principle of Pontryagin
• Applications to control:
Minimum time problems: car-parking minimum time problem; linearized pendulum stabilization problem
Minimum fuel control problem: moon lander