Multiresolution strategies for the numerical solution of optimal control problems

Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a nonlinear programming (NLP) problem that is solved using standard NLP codes. The novelty of the proposed approach hinges on the automatic calculation of a suitable, nonuniform grid over which the NLP problem is solved, which tends to increase numerical efficiency and robustness. Control and/or state constraints are handled with ease, and without any additional computational complexity. The proposed algorithm is based on a simple and intuitive method to balance several conflicting objectives, such as accuracy of the solution, convergence, and speed of the computations. The benefits of the proposed algorithm over uniform grid implementations are demonstrated with the help of several nontrivial examples. Furthermore, two sequential multiresolution trajectory optimization algorithms for solving problems with moving targets and/or dynamically changing environments have been developed.Ph.D.Committee Chair: Tsiotras, Panagiotis; Committee Member: Calise, Anthony J.; Committee Member: Egerstedt, Magnus; Committee Member: Prasad, J. V. R.; Committee Member: Russell, Ryan P.; Committee Member: Zhou, Hao-Mi

Summarizing Text Using Lexical Chains

The current technology of automatic text summarization imparts an important role in the information retrieval and text classification, and it provides the best solution to the information overload problem. And the text summarization is a process of reducing the size of a text while protecting its information content. When taking into consideration the size and number of documents which are available on the Internet and from the other sources, the requirement for a highly efficient tool on which produces usable summaries is clear. We present a better algorithm using lexical chain computation. The algorithm one which makes lexical chains a computationally feasible for the user. And using these lexical chains the user will generate a summary, which is much more effective compared to the solutions available and also closer to the human generated summary

The Shear Viscosity in Anisotropic Phases

We construct anisotropic black brane solutions and analyse the behaviour of some of their metric perturbations. These solutions correspond to field theory duals in which rotational symmetry is broken due an externally applied, spatially constant, force. We find, in several examples, that when the anisotropy is sufficiently big compared to the temperature, some components of the viscosity tensor can become very small in units of the entropy density, parametrically violating the KSS bound. We obtain an expression relating these components of the viscosity, in units of the entropy density, to a ratio of metric components at the horizon of the black brane. This relation is generally valid, as long as the forcing function is translationally invariant, and it directly connects the parametric violation of the bound to the anisotropy in the metric at the horizon. Our results suggest the possibility that such small components of the viscosity tensor might also arise in anisotropic strongly coupled fluids found in nature.Comment: 30 pages + 4 page appendix, 3 figures, added reference