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1. Fault Isolation of a Class of Uncertain Nonlinear Parabolic PDE Systems

   Zhang, Jingting; Yuan, Chengzhi; Stegagno, Paolo; Zeng, Wei (October 2022, Modeling, Estimation and Control Conference)

   This paper proposes a novel fault isolation (FI) scheme for distributed parameter systems modeled by a class of parabolic partial differential equations (PDEs) with nonlinear uncertain dynamics. A key feature of the proposed FI scheme is its capability of dealing with the effects of system uncertainties for accurate FI. Specifically, an approximate ordinary differential equation (ODE) system is first derived to capture the dominant dynamics of the original PDE system. An adaptive dynamics identification approach using radial basis function neural network is then proposed based on this ODE system, to achieve locally-accurate identification of the uncertain system dynamics under faulty modes. A bank of FI estimators with associated adaptive thresholds are finally designed for real-time FI decision making. Rigorous analysis on the fault isolatability is provided. Simulation study on a representative transport-reaction process is conducted to demonstrate the effectiveness of the proposed approach. 

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2. Adaptive NN-Based Boundary Control for Output Tracking of A Wave Equation with Matched and Unmatched Boundary Uncertainties

   https://doi.org/10.23919/ACC53348.2022.9867897  

   Zhang, Jingting; Stegagno, Paolo; Zeng, Wei; Yuan, Chengzhi (June 2022, Proceedings of the American Control Conference)

   This paper is focused on the output tracking control problem of a wave equation with both matched and unmatched boundary uncertainties. An adaptive boundary feedback control scheme is proposed by utilizing radial basis function neural networks (RBF NNs) to deal with the effect of system uncertainties. Specifically, two RBF NN models are first developed to approximate the matched and unmatched system uncertain dynamics respectively. Based on this, an adaptive NN control scheme is derived, which consists of: (i) an adaptive boundary feedback controller embedded by the NN model approximating the matched uncertainty, for rendering stable and accurate tracking control; and (ii) a reference model embedded by the NN model approximating the unmatched uncertainty, for generating a prescribed reference trajectory. Rigorous analysis is performed using the Lyapunov theory and the C0-semigroup theory to prove that our proposed control scheme can guarantee closed-loop stability and wellposedness. Simulation study has been conducted to demonstrate effectiveness of the proposed approach. 

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3. A Novel Quotient Space Approach to Model-Based Fault Detection and Isolation: Theory and Preliminary Simulation Evaluation

   https://doi.org/10.1109/IROS51168.2021.9636026  

   Mao, Annie M.; Whitcomb, Louis L. (September 2021, 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS))

   We report the development of novel fault detection and isolation (FDI) methods for model-based fault detection (MB-FD) and quotient-space fault isolation (QS-FI). This FDI approach performs MB-FD and QS-FI of single or multiple concurrent faults in plants and actuators simultaneously, without a priori knowledge of fault form, type, or dynamics. To detect faults, MB-FD characterizes deviation from nominal behavior using the plant velocity and plant and actuator parameters estimated by nullspace-based adaptive identification. To isolate (i.e. identify) faults, the QS-FI algorithm compares the estimated parameters to a nominal parameter class in progressively decreasing-dimensional quotient spaces of the parameter space. A preliminary simulation study of these proposed FDI methods applied to a three degree-of-freedom uninhabited underwater vehicle plant model shows their ability to detect as well as isolate faults for the cases of both single and multiple simultaneous faults and suggests the generalizability of the MB-FD and QS-FI approaches to any well-defined second-order plant and actuator model whose parameters enter linearly: a broad class of systems which includes aerial vehicles, marine vehicles, spacecraft, and robot arms. 

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4. Fault detection and accommodation of positive real infinite dimensional systems using adaptive RKHS-based functional estimation

   https://doi.org/10.23919/ACC53348.2022.9867405  

   Demetriou, Michael A. (June 2022, 2022 American Control Conference)

   This paper presents an adaptive functional estimation scheme for the fault detection and diagnosis of nonlinear faults in positive real infinite dimensional systems. The system is assumed to satisfy a positive realness condition and the fault, taking the form of a nonlinear function of the output, is assumed to enter the system at an unknown time. The proposed detection and diagnostic observer utilizes a Reproducing Kernel Hilbert Space as the parameter space and via a Lyapunov redesign approach, the learning scheme for the unknown functional is used for the detection of the fault occurrence, the diagnosis of the fault and finally its accommodation via an adaptive control reconfiguration. Results on parabolic PDEs with either boundary or in-domain actuation and sensing are included. 

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5. Discovering sparse interpretable dynamics from partial observations

   https://doi.org/10.1038/s42005-022-00987-z  

   Lu, Peter Y.; Ariño Bernad, Joan; Soljačić, Marin (August 2022, Communications Physics)

   Abstract Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. Achieving this kind of interpretable system identification is even more difficult for partially observed systems. We propose a machine learning framework for discovering the governing equations of a dynamical system using only partial observations, combining an encoder for state reconstruction with a sparse symbolic model. The entire architecture is trained end-to-end by matching the higher-order symbolic time derivatives of the sparse symbolic model with finite difference estimates from the data. Our tests show that this method can successfully reconstruct the full system state and identify the equations of motion governing the underlying dynamics for a variety of ordinary differential equation (ODE) and partial differential equation (PDE) systems. 

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