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- Genre: Masters Thesis
Description
This thesis describes an approach to system identification based on compressive sensing and demonstrates its efficacy on a challenging classical benchmark single-input, multiple output (SIMO) mechanical system consisting of an inverted pendulum on a cart. Due to its inherent non-linearity and unstable behavior, very few techniques currently exist that are capable of identifying this system. The challenge in identification also lies in the coupled behavior of the system and in the difficulty of obtaining the full-range dynamics. The differential equations describing the system dynamics are determined from measurements of the system's input-output behavior. These equations are assumed to consist of the superposition, with unknown weights, of a small number of terms drawn from a large library of nonlinear terms. Under this assumption, compressed sensing allows the constituent library elements and their corresponding weights to be identified by decomposing a time-series signal of the system's outputs into a sparse superposition of corresponding time-series signals produced by the library components. The most popular techniques for non-linear system identification entail the use of ANN's (Artificial Neural Networks), which require a large number of measurements of the input and output data at high sampling frequencies. The method developed in this project requires very few samples and the accuracy of reconstruction is extremely high. Furthermore, this method yields the Ordinary Differential Equation (ODE) of the system explicitly. This is in contrast to some ANN approaches that produce only a trained network which might lose fidelity with change of initial conditions or if facing an input that wasn't used during its training. This technique is expected to be of value in system identification of complex dynamic systems encountered in diverse fields such as Biology, Computation, Statistics, Mechanics and Electrical Engineering.
ContributorsNaik, Manjish Arvind (Author) / Cochran, Douglas (Thesis advisor) / Kovvali, Narayan (Committee member) / Kawski, Matthias (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2011
Description
Navigating within non-linear structures is a challenge for all users when the space is large but the problem is most pronounced when the users are blind or visually impaired. Such users access digital content through screen readers like JAWS which read out the text on the screen. However presentation of non-linear narratives in such a manner without visual cues and information about spatial dependencies is very inefficient for such users. The NSDL Science Literacy StrandMaps are visual layouts to help students and teachers browse educational resources. A Strandmap shows relationships between concepts and how they build upon one another across grade levels. NSDL Strandmaps are non-linear narratives which need to be presented to users who are blind in an effective way. A good summary of the Strandmap can give the users an idea about the concepts that are explained in it. This can help them decide whether to view the map or not. In addition, a preview-based navigation mechanism can help users decide which direction they want to take, based on a preview of upcoming content in each direction. Given a non-linear narrative like a Strandmap which has both text and structure, and a word limit w, the goal of this thesis is to find the best way to create its summary. The following approaches are considered: – Purely Text-based Approach using a Multi-document Text Summarizer – Purely Structure-based Approach using PageRank – Approaches Combining both Text and Structure → CUTS-Based Approach (Topic Segmentation) → PageRank with Content Since no reference summaries for such structures were available, user studies were conducted to evaluate these algorithms. PageRank with Content approach performed the best. Another important conclusion was that text and structure are intertwined in a Strandmap by design.
ContributorsGaur, Shruti (Author) / Candan, Kasim Selcuk (Thesis advisor) / Sundaram, Hari (Committee member) / Davulcu, Hasan (Committee member) / Arizona State University (Publisher)
Created2011
Description
This work considers the design of separating input signals in order to discriminate among a finite number of uncertain nonlinear models. Each nonlinear model corresponds to a system operating mode, unobserved intents of other drivers or robots, or to fault types or attack strategies, etc., and the separating inputs are designed such that the output trajectories of all the nonlinear models are guaranteed to be distinguishable from each other under any realization of uncertainties in the initial condition, model discrepancies or noise. I propose a two-step approach. First, using an optimization-based approach, we over-approximate nonlinear dynamics by uncertain affine models, as abstractions that preserve all its system behaviors such that any discrimination guarantees for the affine abstraction also hold for the original nonlinear system. Then, I propose a novel solution in the form of a mixed-integer linear program (MILP) to the active model discrimination problem for uncertain affine models, which includes the affine abstraction and thus, the nonlinear models. Finally, I demonstrate the effectiveness of our approach for identifying the intention of other vehicles in a highway lane changing scenario. For the abstraction, I explore two approaches. In the first approach, I construct the bounding planes using a Mixed-Integer Nonlinear Problem (MINLP) formulation of the given system with appropriately designed constraints. For the second approach, I solve a linear programming (LP) problem that over-approximates the nonlinear function at only the grid points of a mesh with a given resolution and then accounting for the entire domain via an appropriate correction term. To achieve a desired approximation accuracy, we also iteratively subdivide the domain into subregions. This method applies to nonlinear functions with different degrees of smoothness, including Lipschitz continuous functions, and improves on existing approaches by enabling the use of tighter bounds. Finally, we compare the effectiveness of this approach with the existing optimization-based methods in simulation and illustrate its applicability for estimator design.
ContributorsSingh, Kanishka Raj (Author) / Yong, Sze Zheng (Thesis advisor) / Artemiadis, Panagiotis (Committee member) / Berman, Spring (Committee member) / Arizona State University (Publisher)
Created2018