Översikt

  • Welcome to CHEM-E7225

    (Feb 04) Corrected version of Assignment 1 available in the Assignments section.

    (Feb 07) Assignment 2 available in the Assignments section.

    (Feb 09) Guest seminar `Online optimal control and estimation of large-scale wastewater treatment plants' on Monday Feb 14 at noon (Titanium - C100, Circular Raw Materials Hub).

    (Feb 17) Assignment 3 available in the Assignments section.

    (Feb 25) Remember the extended submission deadline.


    CHEM-E7225 is an introductory course on optimal control

    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 system theory and numerical simulation 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.

    • Introduction/refresher on dynamic process models, numerical simulations, and optimisation  (classes of models, numerical integration schemes, and optimisation problem classes);
    • Root-finding with Newton-type methods (Definitions, convergence rates and contraction)
    • Nonlinear optimisation (Definitions, first- and second-order optimality conditions) and Newton-type algorithms (Equality and inequality constrained problems)
    • Discrete-time optimal control (Formulation and analysis)
    • Dynamic programming (Discrete-time discrete-space problems, linear-quadratic problems, infinite-horizon problems, the linear quadratic regulator)
    • Continuous-time optimal control (Formulation, analysis, and numerical approaches)
    • The Hamilton-Jacobi-Bellman equation (Dynamic programming in continuous-time, linear-quadratic control and Riccati equations) and the Pontryagin maximum principle

    Learning outcomes

    • Discrete-time approximation and simulation of continuous-time differential models
    • Unconstrained and constrained nonlinear programming
    • Discrete- and continuous-time optimal control
    • Online receding-horizon optimal control

    Course evaluation: To pass CHEM-E7225, you must return the solution to all the exercises (80%) and participate (20%) to the course activities. 

    • You get to pick your deadline for returning the exercises. Your deadline must be before DISCUSS DATE (2022) at 23:59:59.
    • Once chosen, you must communicate the deadline to the lecturer via email, and stick to it.
    • You must communicate the chosen deadline by DISCUSS DATE (2022) at 23:59:59 (Do not forget to do it, if you want to pass the course).
    • Delayed submissions will be penalised: Your final score will drop by one (1) Oodi point every 24 hours after deadline.

    Grading scheme (0-100 MC to 0-5 Oodi conversion)

    • 5 <-- [88, 100]
    • 4 <-- [76, 88)
    • 3 <-- [64, 76)
    • 2 <-- [52,64)
    • 1 <-- [40,52)
    • 0 <-- [00,40)

    About the exercises (80%)

    • One (1) written report with your solutions
    • Include your results and your code
    • Include high-quality diagrams
    • Discuss your solution/code
    • Submission in MC

    Upload a single file, only use the PDF format. (If you have work multiple files, merge them. If you use MSWord or else, save as PDF. If you use MSWord or else and you have multiple files, ...).

    About participation (20%)

    • Engage with the course activities
    • Comment on the lecture notes
    • Find and report typos/bugs

    Collaboration policy: We encourage you to collaborate in figuring out answers and help others solve the problems, yet we ask you to submit your work individually and explicitly acknowledge those with whom you collaborated. We are assuming that you take the responsibility to make sure you personally understand the solution to work arising from collaboration.


    Course material: The course is based on lecture slides and hand-written notes; both will be uploaded here. The material is mostly based on the following textbooks:

    • Nocedal, J. and Wright, S. J., Nonlinear optimization, 2006;
    • Boyd, S. and Vandenberghe, L.,  Convex optimization, 2004;
    • 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.

    Some teaching material/figures by D. Bertsekas, S. Gros, M. Diehl, A. Quarteroni, J. Rawlings, and S. Boyd is also used throughout