Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


After the course, the participant will understand:

  • Unconstrained and constrained numerical optimsation (Newton's type methods, automatic differentiation);
  • Discrete-time optimal control (Dynamic programming: Basic, iterative and differential variants);
  • Continuous-time optimal control (Hamilton-Jacobi-Bellman, Pontryagin approaches, direct approaches);
  • On-line optimal control (Model predictive control, moving-horizion estimation and control).


Credits: 5

Schedule: 07.01.2025 - 17.02.2025

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Francesco Corona

Contact information for the course (applies in this implementation):

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English


  • valid for whole curriculum period:

    We study the mathematical principles of optimal control to manipulate the dynamic behaviour of process systems and the numerics used for its solution. The course aims at bringing understanding on how to combine numerical optimisation with dynamical systems theory to formulate and solve optimal control problems in both discrete- and continuous-time. We develop the topic in general application domains in chemical and bio-chemical engineering.

Assessment Methods and Criteria
  • valid for whole curriculum period:

    Home assignments and/or project work, and/or exam.

  • valid for whole curriculum period:

    Lectures (24h) and Exercises (24h)

    Home assignments and independent study (80h)

    Exam (4h)


Study Material
  • valid for whole curriculum period:

    • Nocedal, J. and Wright, S. J., Nonlinear optimization, 2006;
    • Bertsekas, D. P., Dynamic programing and optimal control, vol. I & II, 2017 & 2012;
    • Bertsekas, D. P., Reinforcement learning and optimal control, 2019;
    • Betts, J. T., Practical methods for optimal control and estimation using nonlinear programming, 2009;
    • Rawlings, J. B., Mayne D. Q., Diehl, M., Model predictive control, 2017.

Substitutes for Courses
SDG: Sustainable Development Goals

    3 Good Health and Well-being

    4 Quality Education

    5 Gender Equality

    6 Clean Water and Sanitation

    7 Affordable and Clean Energy

    8 Decent Work and Economic Growth

    9 Industry, Innovation and Infrastructure

    11 Sustainable Cities and Communities

    12 Responsible Production and Consumption

    13 Climate Action


Further Information
  • valid for whole curriculum period:

    Teaching Language: English

    Teaching Period: 2024-2025 Spring III
    2025-2026 Spring III


    A maximum number of 30 students is admitted to the course. Priority is given to degree students taking in Chemical and Metallurgical Engineering MSc programme and the Chemical and Process Engineering major of the Chemical, Biochemical and Materials Engineering MSc programme. If space, other students (exchange students, other Aalto MSc students, doctoral students, etc) will be admitted to the course based on registration order.

    The course implementation may be cancelled if the number of students enrolled to the course implementation does not meet the required minimum of five students. In the case of cancelled course implementations, the students enrolled to them will be provided with an alternative way of completing the course or advised to take some other applicable course.