Fundamentals of Optimal Control Theory

Additional Info

  • ECTS credits: 4
  • Semester: 1
  • University: Brno University of Technology
  • Prerequisites:

    Linear algebra, differential and integral calculus, ordinary differential equations, mathematical programming, calculus of variations.

  • Objectives:

    The aim of the course is to explain basic ideas and results of the optimal control theory, demonstrate the utilized techniques and apply these results to solving practical variational problems.

  • Topics:

    1. The scheme of variational problems and basic task of optimal control theory.

    2. Maximum principle.

    3. Time-optimal control of an uniform motion.

    4. Time-optimal control of a simple harmonic motion.

    5. Basic results on optimal controls.

    6. Variational problems with moving boundaries.

    7. Optimal control of systems with a variable mass.

    8. Optimal control of systems with a variable mass (continuation).

    9. Singular control.

    10. Energy-optimal control problems.

    11. Variational problems with state constraints.

    12. Variational problems with state constraints (continuation).

    13. Solving of given problems.

  • Books:

    [1] Pontrjagin, L. S. - Boltjanskij, V. G. - Gamkrelidze, R. V. - Miščenko, E. F.: Matematičeskaja teorija optimalnych procesov, Moskva, 1961.

    [2] Lee, E. B. - Markus L.: Foundations of optimal control theory, New York, 1967.

  • More information:

    The course familiarises students with basic methods used in the modern control theory. This theory is presented as a remarkable example of the interaction between practical needs and mathematical theories. Also dealt with are the following topics: Optimal control. Pontryagin's maximum principle. Time-optimal control of linear problems. Problems with state constraints. Singular control. Applications.

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