A nonsmooth Newton's method for discretized optimal control problems with state and control constraints
Matthias Gerdts - School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom (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,
Received: March 2007; Revised: September 2007; Available Online: April 2008.
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