This is a course on model predictive control (MPC), or optimal control of systems with hard constraints on states and control inputs. Contents; Properties of discrete-time linear systems in state-space form; optimal state transfer by linear and quadratic programming; design of linear-quadratic optimal controllers using dynamic programming; model predictive control and the receding horizon principle; dealing with state and control constraints; design and tuning of model predictive controllers and receding-horizon estimators; output feedback MPC; reference-following MPC; stability analysis of MPC controllers; implementation as explicit nonlinear feedback law or by real-time optimization.
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Content and learning outcomes
The course gives a thorough treatment of theory and application of model predictive control In particular, the following is treated
- analysis of properties of linear systems in discrete time
- use of linear and quadratic programming to determine open loop control of linear systems in discrete time
- use of dynamic programming to determine optimal observers and linear control systems that minimise quadratic objective functions in the control input and the system states (LQG control)
- the idea behind receding-horizon control and how model predictive control (MPC) expands on LQG to handle hard limitations on control inputs and system states
- design of MPC controllers for technical systems and how different design parameters should be chosen to satisfy the performance requirements that are set on the closed system
- stability properties of MPC controllers
- implementation of MPC controllers either as an explicit non-linear control system (that is determined off-line) or through real time optimization in each sample.
Intended learning outcomes
After passing the course, the student should be able to
- formulate theory and definitions of important concepts in model predictive control.
- apply theory and methods in model predictive control.
Literature and preparations
Automatic Control, general course or permission from the examiner
EL1000 Automatic Control Basic Course, or equivalent
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
- LAB1 - Lab 1, 1.5 credits, grading scale: P, F
- LAB2 - Lab 2, 1.5 credits, grading scale: P, F
- LAB3 - Lab 3, 1.5 credits, grading scale: P, F
- TEN1 - Exam, 3.0 credits, grading scale: A, B, C, D, E, FX, 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.
Other requirements for final grade
LAB1 1.5p Lab 1 Grading scale P/F
LAB2 1.5p Lab 2 Grading scale P/F
LAB3 1.5p Lab 3 Grading scale P/F
TEN1 3p Written examination. Grading scale A-B-C-D-E-Fx-F
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 EL2700
Main field of study
In this course, the EECS code of honor applies, see: