One Step Hybrid Block Method for The Solution of Optimal Control Problems

This paper considers interpolation and collocation approach for the development of hybrid linear multistep method for the solution of optimal control problems modelled in ordinary differential equations (ODEs). ForwardBackward Sweep method was adopted via Pontryagin’s principle. Stability analysis was carried on the developed method and it shows that the developed method is stable, consistent and therefore convergent. Also, numerical examples show that the method compete favourably when compared with the existing method

Range-based people detection and tracking for socially enabled service robots

With a growing number of robots deployed in populated environments, the ability to detect and track humans, recognize their activities, attributes and social relations are key components for future service robots. In this article we will consider fundamentals towards these goals and present several results using 2D range data.We first propose a learning method to detect people in sensory data based on a set of boosted features. The method largely outperforms the state of the art that typically relies on hand-tuned classifiers. Then, we present a person tracking approach based on the detection and fusion of leg tracks. To deal with the frequent occlusion and self-occlusion of legs, we extend a Multi-Hypothesis Tracking (MHT) approach by the ability to explicitly reason about and deal with adaptive occlusion probabilities. Finally, we address the problem of tracking groups of people, a first step towards the recognition of social relations. We further extend the MHT approach by a multiple model hypothesis stage able to reflect split/merge events in group formation processes. The proposed extension is mathematically elegant, runs in real-time and further allows to accurately estimate the number of people in each group. The article concludes with prospects and suggestions for future research

Δr in the Two-Higgs-Doublet Model at full one loop level—and beyond

After the recent discovery of a Higgs-like boson particle at the CERN LHC-collider, it becomes more necessary than ever to prepare ourselves for identifying its standard or non-standard nature. The Electroweak parameter Delta r relating the values of the gauge boson masses [MW,MZ] and the Fermi constant [G_F] is the traditional observable encoding high precision information of the electroweak physics at the quantum level. In this work we present a complete quantitative study of Delta r in the framework of the general (unconstrained) Two-Higgs-Doublet Model (2HDM). First of all we report on a systematic analysis of Delta r at the full one loop level in the general 2HDM, which to our knowledge was missing in the literature. Thereby we extract a theoretical prediction for the mass of the W-boson in this model, taking MZ, \alpha_{em} and G_F as experimental inputs. We find typical corrections leading to mass shifts $\delta MW \sim 20-40 MeV$ which help to improve the agreement with the experimentally measured value, in a degree no less significant than in the MSSM case. In the second part of our study we extend our calculation beyond the mere one-loop order. We devise an effective Lagrangian approach that captures the dominant higher order quantum effects on delta rho (viz. that part of Delta r describing the breaking of the approximate SU(2) custodial symmetry) in the limit of large Higgs boson self-interactions. This limit constitutes a telltale property of the general 2HDM which is unmatched by e.g. the MSSM. Our conclusion is that the Electroweak precision program to be conducted at the LHC, and maybe at a future linear collider, can nicely complement the direct searches. Should these distinctive loop effects be eventually found they would signal a smoking gun hinting at non-standard Higgs physics.Comment: LaTeX, 12 figures, 4 tables. Extended discussion, references added. Version accepted in Eur. Phys. J.