Treffer: Fast numerical methods for mixed--integer nonlinear model--predictive control

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 ...