Computationally efficient trajectory optimization for linear control systems with input and state constraints

Jean François Stumper, Ralph Kennel

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Scopus citations


This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory generation, and the outputs are parameterized using a polynomial basis. A method to parameterize the constraints is introduced using a result on polynomial nonpositivity. The resulting parameterized problem remains linear-quadratic and can be solved using quadratic programming. The problem can be further simplified to a linear programming problem by linearization around the unconstrained optimum. The method promises to be computationally efficient for constrained systems with a high optimization horizon. As application, a predictive torque controller for a permanent magnet synchronous motor which is based on real-time optimization is presented.

Original languageEnglish
Title of host publicationProceedings of the 2011 American Control Conference, ACC 2011
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)9781457700804
StatePublished - 2011

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


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