Journal of Industrial and Management Optimization (JIMO)

A nonsmooth Newton's method for discretized optimal control problems with state and control constraints

Pages: 247 - 270, Volume 4, Issue 2, May 2008      doi:10.3934/jimo.2008.4.247

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Matthias Gerdts - School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom (email)
Martin Kunkel - Department of Mathematics, University of Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany (email)

Abstract: We investigate a nonsmooth Newton's method for the numerical solution of discretized optimal control problems subject to pure state constraints and mixed control-state constraints. The infinite dimensional problem is discretized by application of a general one-step method to the differential equation. By use of the Fischer-Burmeister function the first order necessary conditions for the discretized problem are transformed into an equivalent nonlinear and nonsmooth equation. This nonlinear and nonsmooth equation is solved by a globally convergent nonsmooth Newton's method. Numerical examples for the minimum energy problem and the optimal control of a robot conclude the article.

Keywords:  Optimal control, nonsmooth Newton's method, state constraints, discretization.
Mathematics Subject Classification:  Primary: 49J15, 49J52; Secondary: 49M15.

Received: March 2007;      Revised: September 2007;      Available Online: April 2008.