Technical Briefs

Piecewise Polynomial Control Parameterization in the Direct Solution of Optimal Control Problems

[+] Author and Article Information
Brian C. Fabien

Department of Mechanical Engineering,
University of Washington,Seattle, WA 98195
e-mail: fabien@uw.edu

Manuscript received December 27, 2011; final manuscript received December 7, 2012; published online March 28, 2013. Assoc. Editor: Alexander Leonessa.

J. Dyn. Sys., Meas., Control 135(3), 034506 (Mar 28, 2013) (5 pages) Paper No: DS-11-1407; doi: 10.1115/1.4023401 History: Received December 27, 2011; Revised December 07, 2012

This paper describes an algorithm for the direct solution of a class of optimal control problems. The algorithm is based on approximating the unknown control inputs via a finite dimensional parameterization. Specific control approximations that are implemented include (i) piecewise constant, (ii) piecewise linear, or (iii) piecewise cubic polynomials. The cubic approximation presented here is believed to be new. Another novel feature of the algorithm is that the state equations are approximated using single step Runge–Kutta methods on a fixed mesh. The parameterized optimal control problem is solved using a sequential quadratic programming technique. The paper presents examples to illustrate the convergence behavior of the various control parameterization schemes.

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