Course detail
Optimization Methods II
FSI-VPP-K Acad. year: 2024/2025 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. Project management, CMP and PERT methods. Algorithms for shortest paths in graphs and the branch and bound method. 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. Applications of the methods in solving practical problems.
Language of instruction
Czech
Number of ECTS credits
5
Supervisor
Department
Entry knowledge
Knowledge of the basics of programming, mathematical analysis, algebra, theory of sets, statistics and probability.
Rules for evaluation and completion of the course
Course-unit credit: Active participation in the seminars, elaboration of a given project. Examination: Written and oral.
Attendance at seminars is required. An absence can be compensated for via solving additional problems.
Aims
The aim of the course is to inform the students about creations and applications of mathematical methods for optimal control of technological and economic processes e.g. in the automation of mechanical systems, in the management of production in mechanical engineering, in project management and in optimization of information systems, using contemporary tools of computer science.
Knowledge: Students will know basic principles and algorithms of methods applicable to the optimization of the deterministic and stochastic, discrete and continuous. They will be made familiar with basic principles and algorithms of methods that are appropriate to creation of decision-support systems for project management, as the tool for the identification, selection and realization of projects. Skills: Students will be able to apply the above methods to the solution of the practical problems from economic decision, problems of increasing the reliability of technological devices, problems of automation control of technological processes and problems of project management, by using contemporary tools of computer science.
The study programmes with the given course
Programme N-AIŘ-K: Applied Computer Science and Control, Master's, compulsory
Type of course unit
Guided consultation in combined form of studies
22 hours, compulsory
Teacher / Lecturer
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. Basics of network analysis, topological ordering, CPM.
6. Calculation by stochastic evaluation of activities (PERT method).
7. Algorithms for shortest paths in a graph, the branch and bound method.
8. Multicriteria and constrained optimal control problems.
9. Deterministic continuous time optimal control, Hamilton-Jacobi-Bellman equation, Pontryagin maximum principle.
10. LQR a Kalman filter.
11. Problems with an infinite number of stages.
12. Process scheduling.
13. Approximate dynamic programming and Model predictive control.
Guided consultation
43 hours, optionally
Syllabus
1. Solving dynamic programming problems in Matlab.
2. Resource allocation problems.
3. Dynamic programming in stochastic processes, optimizing a repair schedule.
4. State augmentation, optimal inventory control.
5. Viterbi algorithm, decoding of convolutional codes.
6. Examples of project graphs and networks. Implementation of CPM.
7. Numerical applications of the PERT method.
8. Algorithms for shortest paths in a graph, implementation of the A* algorithm.
9. Implementation of the branch and bound method.
10. Multicriteria knapsack problem.
11. LQR, drone control.
12. Job scheduling.
13. Semestral projects.