15th Triennial World Congress of the International Federation of Automatic Control
  Barcelona, 21–26 July 2002 
HYBRID OPTIMAL CONTROL OF MOTORIZED TRAVELING SALESMEN AND BEYOND
Markus Glocker, Oskar von Stryk
Simulation and Systems Optimization Group, Technische Universit ät
Darmstadt, Alexanderstr. 10, 64283 Darmstadt, Germany
Email: {glocker,stryk}@sim.tu-darmstadt.de
http://www.sim.informatik.tu-darmstadt.de

Numerical methods for optimal control of hybrid dynamical systems are considered where the discrete dynamics and the nonlinear continuous dynamics are tightly coupled. A decomposition approach for numerically solving general mixed-integer continuous optimal control problems (MIOCPs) is discussed. In the outer optimization loop a branch-and-bound binary tree search is used for the discrete variables. The multiple-phase optimal control problems for the continuous state and control variables in the inner optimization loop are solved by a sparse direct collocation transcription method. A genetic algorithm is applied to improve the performance of the branch-and-bound approach by providing a good initial upper bound on the MIOCP performance index. Results are presented for motorized traveling salesmen problems, new benchmark problems in hybrid optimal control.
Keywords: nonlinear hybrid dynamical systems, mixed-integer optimal control, branch-and-bound, direct collocation transcription, sparse sequential quadratic programming, motorized traveling salesmen, genetic algorithm
Session slot T-Th-A06: Behaviour and optimal control of hybrid systems/Area code 5c : Computer Aided Control Systems Design