The "Optimal Control and Identification" is suitable for students of IT and related fields and its goal is to explain the principles of automatic control in a suitable way. The course does not intend to train specialists in controller design but rather to exlpain to the graduates of the course what control means and how to approach various tasks of automatic control.

Doctoral state exam - topics:

1. Tasks of optimal control, static and dynamic optimization of deterministic, stochastic and adaptive control.
2. Dynamac optimization, forms of loss functions, border conditions, Euler-Lagrange equation.
3. Limitation of shapes of control non-equations and Pontrjagin principle of minimum.
4. Dynamic programming, design of loss functions, Hamiltona-Jakobiho-Bellman equation.
5. Linear controller, design of loss function, Riccati equation.
6. Repeating of characteristics of random processes, mean values, dispersion, correlation, covariation, Wiener-Chincin relationships, Parceval theorem, while and "color" noise, transformation of random signals in linear system.
7. Overview of Bayesovs estimations, loss and risk functions, general principle of dynamic filtration.
8. Linear dynamic (Kalman) filter, its design, conversion to discrete filter, generalization of dynamic filter, Wiener filter.
9. Parallel identification of system and trajectory as well as generalized state vector, linearized Kalman filter, contruction of selected non-linear filters.
10. Stochastic control, linear quadratic Gauss problem, continuous and discrete stochastic state regulator and servo mechanism.
11. Adaptive systems, parallel identification of status, parameters, and control, most frequent structures of adaptive systems.
12. Classic methods of regulations.