167 research outputs found
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 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
The Belle II Physics Book
We present the physics program of the Belle II experiment, located on the
intensity frontier SuperKEKB collider. Belle II collected its first
collisions in 2018, and is expected to operate for the next decade. It is
anticipated to collect 50/ab of collision data over its lifetime. This book is
the outcome of a joint effort of Belle II collaborators and theorists through
the Belle II theory interface platform (B2TiP), an effort that commenced in
2014. The aim of B2TiP was to elucidate the potential impacts of the Belle II
program, which includes a wide scope of physics topics: B physics, charm, tau,
quarkonium, electroweak precision measurements and dark sector searches. It is
composed of nine working groups (WGs), which are coordinated by teams of
theorist and experimentalists conveners: Semileptonic and leptonic B decays,
Radiative and Electroweak penguins, phi_1 and phi_2 (time-dependent CP
violation) measurements, phi_3 measurements, Charmless hadronic B decay, Charm,
Quarkonium(like), tau and low-multiplicity processes, new physics and global
fit analyses. This book highlights "golden- and silver-channels", i.e. those
that would have the highest potential impact in the field. Theorists
scrutinised the role of those measurements and estimated the respective
theoretical uncertainties, achievable now as well as prospects for the future.
Experimentalists investigated the expected improvements with the large dataset
expected from Belle II, taking into account improved performance from the
upgraded detector.Comment: 689 page
The CLIC Potential for New Physics
The Compact Linear Collider (CLIC) is a mature option for the future of high
energy physics. It combines the benefits of the clean environment of
colliders with operation at high centre-of-mass energies, allowing to probe
scales beyond the reach of the Large Hadron Collider (LHC) for many scenarios of new physics. This places the CLIC project at a privileged spot in between the precision and energy frontiers, with capabilities that will significantly extend knowledge on both fronts at the end of the LHC era. In this report we review and revisit the potential of CLIC to search, directly and indirectly, for physics beyond the Standard Model
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