Kirches, Christian Fast numerical methods for mixed-integer nonlinear model-predictive control. (English) Zbl 1312.65101 Advances in Numerical Mathematics. Wiesbaden: Vieweg+Teubner; Heidelberg: Univ. Heidelberg (Diss.) (ISBN 978-3-8348-1572-9/pbk; 978-3-8348-8202-8/ebook). xx, 367 p. (2011). The author develops and investigates efficient numerical methods for nonlinear mixed-integer optimal control and model-predictive control problems. His thesis presents a lot of novel results and tools in a number of areas. New algorithms based on Bock’s direct multiple shooting method consist of convexification and relaxation techniques and a real-time iteration scheme. A proof of local contractivity under reasonable assumptions is given. The obtained nonlinear programs are treated as mathematical programs with vanishing constraints. The author develops and describes new tools for solving the arising nonconvex quadratic subproblems such as a new parametric active set method based on strong stationarity, a block structured factorization, and new matrix update techniques for this factorization. All developed algorithms are implemented in two software packages MuShROOM and qpHPSC and their efficiency is demonstrated on several applications, especially on a real-time predictive cruise control problem. The thesis is well written and organized, divided into ten easy to understand sections. Each of them deals with a particular problem. The author describes and analyzes his ideas in detail. The thesis is intended not only for applied mathematicians and engineers interested in optimal control problems but for everybody who wants to learn about new trends in all proposed branches. Reviewer: Ctirad Matonoha (Prague) Cited in 19 Documents MSC: 65K10 Numerical optimization and variational techniques 65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis 90C11 Mixed integer programming 90C20 Quadratic programming 90C30 Nonlinear programming 49J15 Existence theories for optimal control problems involving ordinary differential equations 49M37 Numerical methods based on nonlinear programming Keywords:mixed-integer optimal control; model-predictive control; direct multiple shooting method; nonlinear programming; SQP method; active set method; outer convexification and relaxation; inexact Newton-type method; real-time iteration scheme; local contractivity; MPVC; QPVC; strong stationarity; block structured factorization; matrix update technique; algorithms; software; thesis Software:UMFPACK; Couenne; MA57; Mathematica; QPOPT; LOQO; MuShROOM; qpHPSC PDFBibTeX XMLCite \textit{C. Kirches}, Fast numerical methods for mixed-integer nonlinear model-predictive control. Wiesbaden: Vieweg+Teubner; Heidelberg: Univ. Heidelberg (Diss.) (2011; Zbl 1312.65101) Full Text: DOI Link