Course detail
Optimization Methods II
FSI-VPP-A Acad. year: 2025/2026 Winter semester
The course deals with the following topics: Dynamic programming and optimal control of stochastic processes. Bellman optimality principle as a tool for optimization of multistage processes with a general nonlinear criterion function. Optimum decision policy. Computational aspects of dynamic programming in discrete time. Hidden Markov models and the Viterbi algorithm. Algorithms for shortest paths in graphs. Multicriteria control problems. Deterministic optimal control in continuous time, Hamilton-Jacobi-Bellman equation, Pontryagin maximum principle. LQR and Kalman filter. Process scheduling and planning. Problems with infinitely many stages. Approximate dynamic programming. Heuristic methods for complex problems. Applications of the methods in solving practical problems.
Supervisor
Department
Learning outcomes of the course unit
Prerequisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Language of instruction
English
Aims
Specification of controlled education, way of implementation and compensation for absences
The study programmes with the given course
Programme N-AIŘ-P: Applied Computer Science and Control, Master's
branch ---: no specialisation, 5 credits, compulsory
Type of course unit
Lecture
39 hours, optionally
Syllabus
1. Basics of mathematical processes theory. Bellman optimality principle and dynamic programming.
2. Minimax (robust) formulation. Reformulations and state augmentation.
3. Deterministic finite-state problems. Forward DP algorithm.
4. Hidden Markov models and the Viterbi algorithm.
5. Algorithms for shortest paths in a graph.
6. Multicriteria and constrained optimal control problems.
7. LQR a Kalman filter.
8. Problems with an infinite number of stages.
9. Deterministic continuous-time optimal control, Hamilton-Jacobi-Bellman equation, Pontryagin maximum principle.
10. Process scheduling.
11. Approximate dynamic programming.
12. Rolling horizon and Model predictive control.
13. Heuristics for complex problems – genetic algorithms and ant colony optimization.
Computer-assisted exercise
26 hours, compulsory
Syllabus
The exercise follows the topics discussed in the lecture. The main focus is on the software implementation of the studied methods.