ORCID Identifier(s)

0000-0001-8485-9186

Graduation Semester and Year

2021

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Aerospace Engineering

Department

Mechanical and Aerospace Engineering

First Advisor

Kamesh Subbarao

Abstract

In recent years, uncertainty propagation has emerged as an important research area in the field of dynamical systems. The growing interest in this area arises out of the need to develop computationally efficient approaches to predict the evolution of a system subject to uncertainties. To this end, this dissertation is focused on developing computational frameworks for uncertainty propagation, control, and state estimation of stochastic dynamical systems using the generalized polynomial chaos (gPC) expansion technique. In the first part of this dissertation, the construction of gPC expansion is presented in general. The novelty of this dissertation lies in developing a mixed sparse grid quadrature technique to carry out computationally efficient uncertainty propagation in dynamical systems wherein the random variables are governed by different (or a mixture of) probability distribution types. Additionally, the proposed quadrature technique in the gPC expansion framework is utilized to study the sensitivity of the system output to the uncertain input variables. Subsequently, this work integrates the idea of uncertainty propagation with those of model data-fusion and optimal control theory for state estimation and robust control, respectively, of stochastic systems subject to parametric uncertainties. Furthermore, the stability margin of a group of cooperative unmanned vehicles is examined in a multi-agent system setting. In this regard, a unified framework is proposed to study the consensus of multi-agent systems with multiplicative uncertainties in the feedback path of agents. The proposed technique provides performance indices that measure the robustness of the networked group of agents to gain, phase, and input delay perturbations. Finally, the dissertation studies the consensus problems in multi-agent systems wherein the information exchange between the agents is affected by non-uniform time-varying delays in the network. The proposed frameworks are applied to various benchmark problems and real-world applications, including the motion of satellites in low-Earth orbits, aeroelastic systems, hypersonic reentry of a spacecraft to Earth, synchronization in the states of short-period dynamics of aircraft, among others.

Keywords

Uncertainty propagation, Stochastic dynamical systems, Generalized polynomial chaos expansion, Sensitivity analysis, Stochastic control, Nonlinear filtering, State estimation, Multi-agent systems, Consensus, Graph theory, Stability margin, Time delays

Disciplines

Aerospace Engineering | Engineering | Mechanical Engineering

Comments

Degree granted by The University of Texas at Arlington

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