## Matching Items (6)

In this thesis I introduce a new direction to computing using nonlinear chaotic dynamics. The main idea is rich dynamics of a chaotic system enables us to (1) build better computers that have a flexible instruction set, and (2) carry out computation that conventional computers are not good at it.…

In this thesis I introduce a new direction to computing using nonlinear chaotic dynamics. The main idea is rich dynamics of a chaotic system enables us to (1) build better computers that have a flexible instruction set, and (2) carry out computation that conventional computers are not good at it. Here I start from the theory, explaining how one can build a computing logic block using a chaotic system, and then I introduce a new theoretical analysis for chaos computing. Specifically, I demonstrate how unstable periodic orbits and a model based on them explains and predicts how and how well a chaotic system can do computation. Furthermore, since unstable periodic orbits and their stability measures in terms of eigenvalues are extractable from experimental times series, I develop a time series technique for modeling and predicting chaos computing from a given time series of a chaotic system. After building a theoretical framework for chaos computing I proceed to architecture of these chaos-computing blocks to build a sophisticated computing system out of them. I describe how one can arrange and organize these chaos-based blocks to build a computer. I propose a brand new computer architecture using chaos computing, which shifts the limits of conventional computers by introducing flexible instruction set. Our new chaos based computer has a flexible instruction set, meaning that the user can load its desired instruction set to the computer to reconfigure the computer to be an implementation for the desired instruction set. Apart from direct application of chaos theory in generic computation, the application of chaos theory to speech processing is explained and a novel application for chaos theory in speech coding and synthesizing is introduced. More specifically it is demonstrated how a chaotic system can model the natural turbulent flow of the air in the human speech production system and how chaotic orbits can be used to excite a vocal tract model. Also as another approach to build computing system based on nonlinear system, the idea of Logical Stochastic Resonance is studied and adapted to an autoregulatory gene network in the bacteriophage λ.

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…

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.

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…

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.

The power of science lies in its ability to infer and predict the

existence of objects from which no direct information can be obtained

experimentally or observationally. A well known example is to

ascertain the existence of black holes of various masses in different

parts of the universe from indirect evidence, such as X-ray…

The power of science lies in its ability to infer and predict the

existence of objects from which no direct information can be obtained

experimentally or observationally. A well known example is to

ascertain the existence of black holes of various masses in different

parts of the universe from indirect evidence, such as X-ray emissions.

In the field of complex networks, the problem of detecting

hidden nodes can be stated, as follows. Consider a network whose

topology is completely unknown but whose nodes consist of two types:

one accessible and another inaccessible from the outside world. The

accessible nodes can be observed or monitored, and it is assumed that time

series are available from each node in this group. The inaccessible

nodes are shielded from the outside and they are essentially

``hidden.'' The question is, based solely on the

available time series from the accessible nodes, can the existence and

locations of the hidden nodes be inferred? A completely data-driven,

compressive-sensing based method is developed to address this issue by utilizing

complex weighted networks of nonlinear oscillators, evolutionary game

and geospatial networks.

Both microbes and multicellular organisms actively regulate their cell

fate determination to cope with changing environments or to ensure

proper development. Here, the synthetic biology approaches are used to

engineer bistable gene networks to demonstrate that stochastic and

permanent cell fate determination can be achieved through initializing

gene regulatory networks (GRNs) at the boundary between dynamic

attractors. This is experimentally realized by linking a synthetic GRN

to a natural output of galactose metabolism regulation in yeast.

Combining mathematical modeling and flow cytometry, the

engineered systems are shown to be bistable and that inherent gene expression

stochasticity does not induce spontaneous state transitioning at

steady state. By interfacing rationally designed synthetic

GRNs with background gene regulation mechanisms, this work

investigates intricate properties of networks that illuminate possible

regulatory mechanisms for cell differentiation and development that

can be initiated from points of instability.

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…

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.

The goal of this thesis research is to contribute to the design of set-valued methods, i.e., algorithms that leverage a set-theoretic framework that can provide a powerful means for control designs for general classes of uncertain nonlinear dynamical systems, and in particular, to develop set-valued algorithms for constrained reachability problems…

The goal of this thesis research is to contribute to the design of set-valued methods, i.e., algorithms that leverage a set-theoretic framework that can provide a powerful means for control designs for general classes of uncertain nonlinear dynamical systems, and in particular, to develop set-valued algorithms for constrained reachability problems and estimation.I propose novel fixed-order hyperball-valued observers for different classes of nonlinear systems, including Linear Parameter Varying, Lipschitz continuous and Decremental Quadratic Constrained nonlinearities, with unknown inputs that simultaneously find bounded sets of states and unknown inputs that contain the true states and inputs and are compatible with the measurement/outputs. In addition, I provide sufficient conditions for the existence and stability of the estimates, the convergence of the estimation errors, and the optimality of the observers.

Moreover, I design state and unknown input observers, as well as mode detectors for hidden mode, switched linear and nonlinear systems with bounded-norm noise and unknown inputs. To address this, I propose a multiple-model approach to obtain a bank of mode-matched set-valued observers in combination with a novel mode observer, based on elimination. My mode elimination approach uses the upper bound of the norm of to-be-designed residual signals to remove inconsistent modes from the bank of observers. I also provide sufficient conditions for mode detectability.

Furthermore, I address the problem of designing interval observers for partially unknown nonlinear systems, using affine abstractions, nonlinear decomposition functions, and a data-driven function over-approximation approach to over-estimate the unknown dynamic model. The proposed observer recursively computes the correct interval estimates. Then, using observed measurement signals, the observer iteratively shrinks the intervals. Moreover, the observer updates the over-approximation model

of the unknown dynamics.

Finally, I propose a tractable family of remainder-from decomposition functions for

a broad range of dynamical systems. Moreover, I introduce a set-inversion algorithm that along with the proposed decomposition functions have several applications, e.g., in the approximation of the reachable sets for bounded-error, constrained, continuous, and/or discrete-time systems, as well as in guaranteed state estimation. Leveraging mixed-monotonicity, I provide novel set-theoretic approaches to address the problem of polytope-valued state estimation in bounded-error discrete-time nonlinear systems, subject to nonlinear observations/constraints.