12. Optimum control

The control problem can be solved in two different ways: pole placement, studied in paragraph 9.3, and optimal control, which consists in finding u that minimizes a certain functional. Depending on the choice of functional, there are several optimal control problems.

• Iterative Learning Control (ILC) consists in making y as neighborly as possible to a given function f. This leads to the minimization problem min _u ││y – f ││.

  Since y = Cx, this problem is implicitly equivalent to solving the system of linear equations: Cx = f, i.e. C ^T Cx = C ^T f.

  In general, this system is ill-conditioned, and a small variation in the data f can lead to a large variation in...