The overall goal is to provide an understanding of the main results in optimal control and how they are used in various applications in engineering, economics, logistics, and biology.
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Content and learning outcomes
Dynamic programming in continuous and discrete time. Hamilton-Jacobi-Bellman equation. Theory of ordinary differential equations. The Pontryagin maximum principle. Linear quadratic optimization. Model predictive control. Infinite horizon optimal control problems. Sufficient conditions for optimality. Numerical methods for optimal control problems.
Intended learning outcomes
To pass the course, the student should be able to do the following:
Describe how the dynamic programming principle works (DynP) and apply it to discrete optimal control problems over finite and infinite time horizons.
Use continuous time dynamic programming and the associated Hamilton-Jacobi-Bellman equation to solve linear quadratic control problems.
Use the Pontryagin Minimum Principle (PMP) to solve optimal control problems with control and state constraints.
Use Model Predictive Control (MPC) to solve optimal control problems with control and state constraints. You should also be able understand the difference between the explicit and implicit MPC control and explain their respective advantages.
Formulate optimal control problems on standard form from specifications on dynamics, constraints and control objective. In addition be able to explain how various control objectives affect the optimal performance.
Explain the principles behind the most standard algorithms for numerical solution of optimal control problems and use Matlab to solve fairly simple but realistic problems.
Integrate the tools learnt during the course and apply them to more complex problems.
Explain how PMP and DynP relates to each other and know their respective advantages and disadvantages. In particular, be able to describe the difference between feedback control versus open loop control and also be able to compare PMP and DynP with respect to computational complexity.
Combine the mathematical methods used in optimal control to derive the solution to variations of the problems studied in the course.
Literature and preparations
A Master degree including at least 30 university credits (hp) in in Mathematics (Calculus, Linear algebra, Differential equations and transform method), and further at least 6 hp in Mathematical Statistics, 6 hp in Numerical analysis and 6 hp in Optimization.
Compendium from the department.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
- TEN1 - Written exam, 7.5 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Project, written examination, exercises.
Other requirements for final grade
Project, written examination.
Optional homeworks give bonus credits on written examination
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.Course web FSF3852