Comparison of Regression Methods on Data-Driven Controller Design for Systems with Observation Noise

Author(s):  
Yoichiro Ashida
Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 949
Author(s):  
Keita Hara ◽  
Masaki Inoue

In this paper, we address the data-driven modeling of a nonlinear dynamical system while incorporating a priori information. The nonlinear system is described using the Koopman operator, which is a linear operator defined on a lifted infinite-dimensional state-space. Assuming that the L2 gain of the system is known, the data-driven finite-dimensional approximation of the operator while preserving information about the gain, namely L2 gain-preserving data-driven modeling, is formulated. Then, its computationally efficient solution method is presented. An application of the modeling method to feedback controller design is also presented. Aiming for robust stabilization using data-driven control under a poor training dataset, we address the following two modeling problems: (1) Forward modeling: the data-driven modeling is applied to the operating data of a plant system to derive the plant model; (2) Backward modeling: L2 gain-preserving data-driven modeling is applied to the same data to derive an inverse model of the plant system. Then, a feedback controller composed of the plant and inverse models is created based on internal model control, and it robustly stabilizes the plant system. A design demonstration of the data-driven controller is provided using a numerical experiment.


2017 ◽  
Vol 50 (1) ◽  
pp. 10889-10894 ◽  
Author(s):  
T.D. Gupta ◽  
H. Habibullah ◽  
H.R. Pota ◽  
I.R. Petersen

2021 ◽  
pp. 1-40
Author(s):  
Yuangang Pan ◽  
Ivor W. Tsang ◽  
Yueming Lyu ◽  
Avinash K Singh ◽  
Chin-Teng Lin

Driver mental fatigue leads to thousands of traffic accidents. The increasing quality and availability of low-cost electroencephalogram (EEG) systems offer possibilities for practical fatigue monitoring. However, non-data-driven methods, designed for practical, complex situations, usually rely on handcrafted data statistics of EEG signals. To reduce human involvement, we introduce a data-driven methodology for online mental fatigue detection: self-weight ordinal regression (SWORE). Reaction time (RT), referring to the length of time people take to react to an emergency, is widely considered an objective behavioral measure for mental fatigue state. Since regression methods are sensitive to extreme RTs, we propose an indirect RT estimation based on preferences to explore the relationship between EEG and RT, which generalizes to any scenario when an objective fatigue indicator is available. In particular, SWORE evaluates the noisy EEG signals from multiple channels in terms of two states: shaking state and steady state. Modeling the shaking state can discriminate the reliable channels from the uninformative ones, while modeling the steady state can suppress the task-nonrelevant fluctuation within each channel. In addition, an online generalized Bayesian moment matching (online GBMM) algorithm is proposed to online-calibrate SWORE efficiently per participant. Experimental results with 40 participants show that SWORE can maximally achieve consistent with RT, demonstrating the feasibility and adaptability of our proposed framework in practical mental fatigue estimation.


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