Regularized and Nonparametric Approaches in System Identification and Data-Driven Control

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Author

Yin, Mingzhou

Date

2024

Type

Doctoral Thesis

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Abstract

This thesis delves into regularized and nonparametric approaches in system identification and data-driven control. Classical model-based control design relies on a compact parametric model structure, which is difficult to obtain for modern complex systems. To address this challenge, regularized approaches adopt general high-dimensional model structures and apply sparse learning and kernel learning theories to identify models by leveraging the sparsity and smoothness properties of the system, respectively. In sparse learning, atomic norm regularization is employed to learn the sparse pole locations of the system within the unit disk. A novel algorithm is presented to solve the associated infinite-dimensional sparse learning problem. Debiasing and stability selection algorithms are applied to enhance the identification performance as well. In kernel learning, a multiple kernel design with optimal first-order kernels is proposed to identify the impulse response of the system. This enforces a low-complexity model structure while maintaining the favorable bias-variance trade-off property of kernel learning. More reliable error bounds, associated with the Gaussian process interpretation of kernel learning, are derived when hyperparameters are unknown, supporting safety-critical applications. An alternative path to circumvent model structure selection is to construct nonparametric predictors that predict output trajectories. This can be done by characterizing possible system behaviors as linear combinations of deterministic trajectory data. Extensions of this approach to stochastic data are investigated. A novel algorithm is developed to denoise the data by solving a low-rank Hankel matrix denoising problem. It achieves a more substantial noise reduction than existing algorithms. A maximum likelihood predictor, dubbed the signal matrix model, is derived to establish a statistical framework that provides accurate prediction in the presence of noise without requiring sophisticated tuning. Prediction error quantification associated with the nominal prediction is also provided. The proposed predictor can be directly applied to receding horizon predictive control, replacing model-based predictors, with the possibility to incorporate online data. It demonstrates superior performance compared to existing data-driven predictors. The algorithm is further extended to the stochastic control framework with initial condition estimation and guaranteed constraint satisfaction. Its effectiveness in practice is validated through high-fidelity simulation of a space heating control case study. Specific identification approaches for periodic systems are also studied. Linear time-periodic systems are identified by reformulating them into switched systems and extending the atomic norm regularization approach with grouped variables. In the frequency domain, a novel subspace identification algorithm is proposed by estimating the time-aliased periodic impulse response from the frequency response of the lifted system. Periodic models can also be utilized to identify local limit cycle dynamics. This is accomplished by linearizing the system along the limit cycle and estimating the periodic dynamics matrix of the linearized system by kernel learning. The approach is tested on an airborne wind energy system. Show more

Permanent link

https://doi.org/10.3929/ethz-b-000666885

Publication status

published

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Contributors

Examiner: Smith, Roy

Examiner: Dörfler, Florian

Examiner: Chiuso, Alessandro

Publisher

ETH Zurich

Organisational unit

08814 - Smith, Roy (Tit.-Prof.) (ehemalig) / Smith, Roy (Tit.-Prof.) (former)
09478 - Dörfler, Florian / Dörfler, Florian

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