Rajiv Singh PhD Dissertation Defense

Name:
Rajiv Singh

Title:
Interpolation and Convexification Methods for Tractable Learning of Dynamic Systems

Date:
9/9/2024

Time:
9:00:00 AM

Location: https://northeastern.zoom.us/j/97729968899?pwd=WfExrC0k60ocNpzCrkJXK3HyJDptMK.1

Committee Members:
Prof. Mario Sznaier (Advisor)

Prof. Lennart Ljung

Prof. Octavia Camps,
Prof. Stratis Ioannidis

Abstract:
In this thesis, we present interpolation and convexification based system identification techniques that are geared towards producing, practical, engineering-friendly models. The models are either linear, or close to being linear – they are either weakly nonlinear, are described by a switching among linear models, or linear models whose parameters are allowed to depend upon certain states or inputs or the system. A common objective in all the proposed approaches is to determine the lowest-order models that are consistent with the information available in the form of data and available priors. We leverage ideas from the rational interpolation community in order to create tractable algorithms that are efficient and often scale well with the amount of data. In addition, we present control-oriented learning methods extend the basic approaches by directly incorporating the closed-loop objectives. The resulting models are self-certified in that they produce certificates of guaranteed closed-loop behavior.

A summary of the essential ideas presented in this thesis follows next.
1. Using the rank-revealing properties of Loewner and Hankel matrices, we develop a convex algorithm for identification of low order stable transfer functions using time and frequency domain data. This results are guaranteed to meet prescribed worst case bounds.

2. We propose a set of techniques geared towards control-oriented identification of potentially unstable linear models using open-loop data. These models come with a certification of robust stabilizability which greatly aids the control design procedure. The first technique leverages the concept of coprime factors of a linear system while the second technique uses robust identification of a system’s predictor as a vehicle towards identification of the plant model. The latter technique also directly incorporates the closed-loop objective of νgap minimization into the identification procedure.

3. We present convex approaches to identification of nonlinear polynomial models with time-varying coefficients. The model coefficients evolution is governed by scheduling maps that are described by low-order linear differential equations. A first approach uses a Hankel matrix rank minimization technique towards a joint identification of the model’s parameters and the scheduling map. A second approach leverages the atomic norm minimization framework to extend the first approach to bilinear systems, and also support easy incorporation of scheduling priors.

4. We present some results regarding sparse identification of Nonlinear ARX models incorporating bounded nonlinear maps. We present approaches to achieve sparsity with respect to the number of regressors used, and with respect to the maximum lag employed by any of the contributing regressors. The proposed algorithm leverages ideas from sparse learning and ensemble learning for sparse NARX models.

5. We present a new framework for identification of switched linear and parameter-varying systems based on rational interpolation. We develop multivariate interpolation procedures based on the recent “block-AAA” algorithms. We demonstrate that this modeling framework leads to fast, accurate, and scalable algorithms that can be used in various settings where the data domain is described by correlations, frequency, or scheduling variables.