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Stochastic Motion Planning for Diffusions & Fault Detection and Isolation for Large Scale Nonlinear Systems


P. Mohajerin Esfahani


The main theme of this thesis is twofold. First, we study a class of specifications, mainly the reachability type questions, in the context of controlled diffusion processes. The second part of the thesis is centered around the fault detection and isolation (FDI) problem for large scale nonlinear dynamical systems. Reachability is a fundamental concept in the study of dynamical systems, and in view of applications of this concept ranging from engineering, manufacturing, biology, and economics, to name but a few, has been studied extensively in the control theory literature. One particular problem that has turned out to be of fundamental importance in engineering is the so-called ``\emph{reach-avoid}" problem. In the deterministic setting this problem consists of determining the set of initial conditions for which one can find at least one control strategy to steer the system to a target set while avoiding certain obstacles. The focus of the first part in this thesis is on the stochastic counterpart of this problem with an extension to more sophisticated maneuvers which we call the ``\emph{motion planning}" problem. From the technical standpoint, this part can be viewed as a theoretical bridge between the desired class of specifications and the existing numerical tools (e.g., partial differential equation (PDE) solvers) that can be used for verification and control synthesis purposes. The second part of the thesis focuses on the FDI problem for large scale nonlinear systems. FDI comprises two stages: residual generation and decision making; the former is the subject addressed here. The thesis presents a novel perspective along with a scalable methodology to design an FDI filter for high dimensional nonlinear systems. Previous approaches on FDI problems are either confined to linear systems, or they are only applicable to low dimensional dynamics with specific structures. In contrast, we propose an optimization-based approach to robustify a linear residual generator given some statistical information about the disturbance signatures, shifting attention from the system dynamics to the disturbance inputs. The proposed scheme provides an alarm threshold whose performance is quantified in a probabilistic fashion. From the technical standpoint, the proposed FDI methodology is effectively a relaxation from a robust formulation to probabilistic constraints. In this light, the alarm threshold obtained via the optimization program has a probabilistic performance index. Intuitively speaking, one would expect to improve the false alarm rate by increasing the filter threshold. The goal of the last part of the thesis is to quantify this connection rigorously. Namely, in a more general setting including a class of non-convex problems, we establish a theoretical bridge between the optimum values of a robust program and its randomized counterpart. The theoretical results of this part are finally deployed to diagnose and mitigate a cyber-physical attack introduced by the interaction between IT infrastructure and power system.


Type of Publication:

(03)Ph.D. Thesis

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% Autogenerated BibTeX entry
@PhDThesis { Xxx:2014:IFA_4834,
    author={P. Mohajerin Esfahani},
    title={{Stochastic Motion Planning for Diffusions \& Fault
	  Detection and Isolation for Large Scale Nonlinear Systems}},
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