OPTEC - K.U.Leuven Center of Excellence: Optimization in Engineering

Direct and indirect methods for optimal control problems and applications in engineering
Matthias Gerdts, School of Mathematics, University of Birmingham



Abstract:

The talk discusses numerical methods for optimal control problems with ordinary differential equations and shows how they can be extended to mixed-integer optimal control problems and real-time optimal control problems.

The first part of the talk is concerned with two different approaches for the numerical solution of optimal control problems: the direct discretization approach and a semismooth Newton method. The direct discretization approach transforms the optimal control problem into a nonlinear program which is solved by an SQP method and turns out to be very powerful in practice. The semismooth Newton method is a variant of Newton's method for nonlinear equations and aims at satisfying the first order necessary optimality conditions of the optimal control problem using a nonlinear complementarity function. It possesses good convergence properties and turns out to be particularly well-suited for problems with mixed control-state constraints.

The second part of the talk briefly discusses extensions towards real-time optimization using a sensitivity analysis and mixed-integer optimal control problems using a suitable time transformation.

Finally numerical results for selected applications from aerospace engineering, PDE control and vehicle simulation will be presented.

The organisers gratefully acknowledge the financial support of ICCOS
Download the slides of the talk
Some movies shown during the talk are available at: http://web.mat.bham.ac.uk/M.Gerdts/movies.htm