Preconditioning complex symmetric linear systems

A new polynomial preconditioner for symmetric complex linear systems based on Hermitian and skew-Hermitian splitting (HSS) for complex symmetric linear systems is herein presented. It applies to Conjugate Orthogonal Conjugate Gradient (COCG) or Conjugate Orthogonal Conjugate Residual (COCR) iterative solvers and does not require any estimation of the spectrum of the coefficient matrix. An upper bound of the condition number of the preconditioned linear system is provided. Moreover, to reduce the computational cost, an inexact variant based on incomplete Cholesky decomposition or orthogonal polynomials is proposed. Numerical results show that the present preconditioner and its inexact variant are efficient and robust solvers for this class of linear systems. A stability analysis of the method completes the description of the preconditioner.Comment: 26 pages, 4 figures, 4 table

Comparison of direct and indirect methods for minimum lap time optimal control problems

Minimum lap time simulations are especially important in the design, optimisation and setup of race vehicles. Such problems usually come in different flavours, e.g. quasi-steady state models vs full dynamic models and pre-defined (fixed) trajectory problems vs free trajectory problems. This work is focused on full dynamic models with free trajectory. Practical solution techniques include direct methods (i.e. solution of an NLP problem, widespread approach) and indirect method (i.e. based on Pontryagins principle, less common, yet quite efficient in some cases). In this contribution the performance of the direct and indirect methods are compared in a number of vehicle related problems

Proceedings of IMECE

ABSTRACT In the last years a great effort has been devoted to the development of autonomous vehicles able to drive in a high range of speeds in semi-structured and unstructured environments. This article presents and discusses the software framework for Hardware-In-the-Loop (HIL) and Software-In-the-Loop (SIL) analysis that has been designed for developing and testing of control laws and mission functionalities of semi-autonomous and autonomous vehicles. The ultimate goal of this project is to develop a robotic system, named RUMBy, able to autonomously plan and execute accurate optimal manoeuvres both in normal and in critical driving situations and to be used as a test platform for advanced decision and autonomous driving algorithms. RUMBy's hardware is a 1:6 scale gasoline engine R/C car with onboard telemetry and control systems. RUMBy's software consists of three main modules: the manager module that coordinates the other modules and take high level decision; the motion planner module which is based on a Nonlinear Receding Horizon Control (NRHC) algorithm; the actuation module that produces the driving command for the vehicle. The article describes the details of RUMBy architecture and discusses its modular configuration that easily allows HIL and SIL tests