Sparse and Low-Rank Optimization Techniques for Virtual Sensing and System Identification

This work focuses on two primary topics: (i) the identification of low-order systems and (ii) the design of virtual sensing techniques concerned with learning signals and systems from data. To incorporate prior knowledge or assumptions about unknown signals and systems, sparse and low-rank optimization techniques are adopted. Examples of such prior information include assumptions about signal smoothness, sparse signal representations, or the system being of low order.
One of the primary challenges in system identification is managing the tradeoff between model complexity and predictive accuracy. Simpler models are often preferred if they retain sufficient predictive power. Thus, the problem of low-order output-error system identification has been studied and solved using low-rank optimization techniques. In virtual sensing, the difficulty lies in incorporating prior information about unknown signals while ensuring the problem remains solvable in practice. Thus, this work presents real-time methods for solving the simultaneous input-and-state estimation problem.
This dissertation summarizes the methods, algorithms, and theory presented in Papers I–IX and offers a collection of problem formulations relevant to constrained system identification and virtual sensing.