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

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2 Author(s)
Jean-Fran├žois Stumper ; Institute of Electrical Drive Systems and Power Electronics, Department of Electrical Engineering and Information Technology, Technische Universität München, Arcisstr. 21, D- 80333 Munich, Germany ; Ralph Kennel

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.

Published in:

Proceedings of the 2011 American Control Conference

Date of Conference:

June 29 2011-July 1 2011