- Title
- Innovative data-driven modeling and control for nonlinear systems using Volterra series
- Creator
- Stoddard, Jeremy G.
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2019
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- The Volterra series is a powerful and versatile tool which can be used to model any nonlinear dynamical system that is time-invariant and has fading memory. The popularity of the series in system identification and control applications has been limited due to its complex multidimensional nature, and thus the large numbers of parameters required in a Volterra series model. Recent developments using Bayesian regularization techniques have increased the feasibility of Volterra series estimation from arbitrary time domain data records, however there are still several challenges remaining to enable widespread use of the series in identification and control. Three of these challenges in particular form the motivation for contributions in this thesis. The first challenge addressed in the thesis relates to Volterra series estimation from time domain data, and in particular when data records are short, noisy and arbitrary in nature. While the recently proposed Bayesian regularization approach represents significant progress, the method is still generally inaccurate or computationally intractable for series orders higher than 3. Two main factors cause these issues at high series orders, and they are the computational burden of the Bayesian optimization routine, and the sheer number of parameters required to be estimated. To combat these issues, a new expectation-maximization (EM) framework is proposed in this thesis to improve the computation time scaling (with series order) of the optimization problem. The new framework is then combined with a basis function approach to estimation, where the Volterra series terms are estimated using orthonormal basis function expansions. Simulation and practical examples highlight the improved feasibility and performance of the regularized basis function approach over existing methods in the literature. The second motivating challenge is to construct equivalent regularized methods for frequency domain identification of Volterra series models. There are several frequency domain representations available in the literature for Volterra series, and two of these models are considered in the thesis: Nonlinear Output Frequency Response Functions (NOFRFs) and Generalized Frequency Response Functions (GFRFs). An extension to the linear theory is proposed for estimating NOFRFs in the case where the system has a parallel Hammerstein structure. In this case, the NOFRF at each nonlinear order behaves like a linear filter. For the GFRFs, which are multidimensional analogs of the time domain Volterra series terms, a Bayesian estimation method is developed and designed to be equivalent to the time domain method available in the literature. Simulation examples confirm the benefits of each model's proposed method. An investigation is also performed to analyze the transient contributions in a nonlinear system's frequency domain response under arbitrary excitation. Analytic expressions are obtained in a highly structured manner, revealing valuable insight for frequency domain estimation. The final challenge considered in the thesis pertains to model-based control. In particular, past results on control using Volterra series models have been limited to a maximum series order of 2 or 3, due to the feasibility of estimation and also because of the complexity of analysis and computation in the controller. In this thesis, a computationally efficient model predictive control (MPC) algorithm is developed for arbitrary order Volterra models expressed using Laguerre basis function expansions. Using a novel Kronecker algebra framework for the state space representation, the online control problem is shown to reduce to a polynomial root-finding problem at each time step. Simulation and practical control studies are conducted to provide evidence of the algorithm's performance.
- Subject
- nonlinear; identification; control; Volterra series
- Identifier
- http://hdl.handle.net/1959.13/1408689
- Identifier
- uon:35873
- Rights
- Copyright 2019 Jeremy G. Stoddard
- Language
- eng
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| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT01 | Thesis | 32 MB | Adobe Acrobat PDF | View Details Download | ||
| View Details Download | ATTACHMENT02 | Abstract | 934 KB | Adobe Acrobat PDF | View Details Download |