This dissertation is principally concerned with the combined state and parameter estimation problem, where the goal is to estimate the state of a discrete-time, linear time-invariant system with uncertainties in the system dynamics. First, we prove necessary and sufficient conditions for the identifiability of unknown parameters within a state-space realization. Next, we evaluate the performance of classical techniques for solving the combined state and parameter estimation problem. We then formulate and test the retrospective cost parameter estimation algorithm under the assumption that the initial states are known. Two variants of the retrospective cost parameter estimation and smoothing algorithm is formulated and tested for the case where the initial states are unknown. Finally, the retrospective cost Kalman filter algorithm is formulated and tested for state estimation despite uncertain noise covariances and potentially nonzero mean sensor and process noises.


Dissertation Committee:

Chair: Dennis S. Bernstein
Cognate Member: Jeffrey Stein
Members: Ilya V. Kolmanovsky, Henry Sodano


Publications:

Journal Papers
“Identifiability of State Space Realizations with Structured Uncertainty”; Submitted to IEEE L-CSS Letters (2017), under review

“Retrospective Cost Subsystem Estimation and Smoothing for Linear Systems with Structured Uncertainty”; Submitted to AIAA JAIS (2017), under review

Conference Papers
“Combined State and Parameter Estimation and Identifiability of State Space Realizations”; IEEE Conference on Decision and Control (2016)

“Exploration and Mapping of an Unknown Flight Envelope”; IEEE Conference on Decision and Control (2014)

“Retrospective Cost Model Refinement for Aircraft Fault Signature Detection”; IEEE American Controls Conference (2014)

“Retrospective Cost Adaptive Control of the NASA Generic Transport Model with Unknown Control-Surface Faults”; AIAA Guidance, Navigation, and Controls Conference (2013)

“Trim-Commanded Adaptive Control for Waypoint-Defined Trajectory Following”; AIAA Guidance, Navigation, and Controls Conference (2013)