Robust controllability of linear systems: Analysis and application to pursuit problems

Robust controllability conditions for a linear uncertain system are derived. A class of transferring strategies is obtained. A robust controllability set, respecting a given control constraint, is constructed. An application example is presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Upper Bounds of the Pursuer Control Based on a Linear-Quadratic Differential Game

Differential game formulations provide an adequate basis for a guidance law synthesis against highly maneuvering targets. This paper deals with a guidance law based on a linear-quadratic differential game formulation. This guidance law has many attractive properties: it is continuous, linear with respect to the state variables, and its gain coefficients can be precalculated offline. Nevertheless, due to the lack of hard control constraints in the formulation, the magnitude of the control can exceed the admissible level imposed by the nature of the problem. In this paper, the upper bound of the interceptor control is obtained depending on the system parameters and the penalty coefficients of the game performance index. It is shown that the interceptor can guarantee an arbitrarily small miss distance without exceeding the control constraints if it has sufficient maneuverability and if the penalty coefficients are chosen properly. By manipulating the penalty coefficients, it is possible to reduce significantly the maneuverability requirements compared to the case of zero interceptor penalty coefficient.     

On the Inverse Problem for Robust Capture Zone Construction

An interception problem with variable velocities and variable lateral acceleration boundaries is considered. Two problems, inverse to constructing the capture zone for a given linear strategy, are formulated. In the first (weak) formulation, a linear strategy is derived forcing its capture zone to contain a given set. In the second (strong) formulation, the capture zone of such a linear strategy is forced to coincide with a given set. A step-by-step algorithm, solving these problems, is derived. This algorithm is based on a detailed differential-geometrical analysis of the capture zone boundary. Illustrative examples are presented.     

Proficiency testing: binary data analysis

A method for evaluating qualitative proficiency testing (PT) of laboratories conducting binary tests is proposed. The method is based on the scale-invariant item response model proposed by the authors in earlier publications. We consider the case where the laboratories under the PT conduct test consisting of a set of test items/species presenting different, but unknown beforehand levels of difficulty when trying to detect a particular property of theirs, and we need to evaluate/compare both the intrinsic abilities of the participating laboratories and the level of difficulty of the test items. We assume that the responses to different test items do not affect one another and discuss how to get and interpret the most likely estimates/scores. The method is illustrated by the example presented in a recent publication by our colleagues from QuoData GmbH and can be considered as an alternative to that proposed in their publication method of scoring.