TY  - GEN
KW  - Modell-prädiktive Regelungmixed-integer optimizationn 
KW  -  nonlinear model predictive control 
KW  -  optimal control 
KW  -  quadratic programming
TI  - Fast numerical methods for mixed--integer nonlinear model--predictive control
Y1  - 2010///
ID  - heidok11636
N2  - This thesis aims at the investigation and development of fast numerical methods for nonlinear mixed--integer optimal control and model- predictive control problems. A new algorithm is developed based on the  direct multiple shooting method for optimal control and on the idea of  real--time iterations, and using a convex reformulation and relaxation  of dynamics and constraints of the original predictive control problem. This algorithm relies on theoretical results and is based on a nonconvex SQP method and a new active set method for nonconvex parametric quadratic programming. It achieves real--time capable control feedback though block structured linear algebra for which we develop new matrix  updates techniques. The applicability of the developed methods is  demonstrated on several applications. This thesis presents novel results and advances over previously  established techniques in a number of areas as follows: We develop a new algorithm for mixed--integer nonlinear model- predictive control by combining Bock's direct multiple shooting method,  a reformulation based on outer convexification and relaxation of the  integer controls, on rounding schemes, and on a real--time iteration  scheme. For this new algorithm we establish an interpretation in the framework  of inexact Newton-type methods and give a proof of local contractivity  assuming an upper bound on the sampling time, implying nominal stability  of this new algorithm. We propose a convexification of path constraints directly depending on  integer controls that guarantees feasibility after rounding, and  investigate the properties of the obtained nonlinear programs. We show  that these programs can be treated favorably as MPVCs, a young and  challenging class of nonconvex problems. We describe a SQP method and develop a new parametric active set  method for the arising nonconvex quadratic subproblems. This method is  based on strong stationarity conditions for MPVCs under certain  regularity assumptions. We further present a heuristic for improving  stationary points of the nonconvex quadratic subproblems to global  optimality. The mixed--integer control feedback delay is determined by the  computational demand of our active set method. We describe a block  structured factorization that is tailored to Bock's direct multiple  shooting method. It has favorable run time complexity for problems with  long horizons or many controls unknowns, as is the case for mixed- integer optimal control problems after outer convexification. We develop new matrix update techniques for this factorization that  reduce the run time complexity of all but the first active set iteration  by one order. All developed algorithms are implemented in a software package that  allows for the generic, efficient solution of nonlinear mixed-integer optimal control and model-predictive control problems using the  developed methods. 
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/11636/
AV  - public
A1  - Kirches, Christian
ER  -