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1. A Hybrid Filtered Basis Functions Approach for Tracking Control of Linear Systems with Unmodeled Nonlinear Dynamics

   https://doi.org/10.1109/CASE49439.2021.9551476  

   Chou, Cheng-Hao; Duan, Molong; Okwudire, Chinedum E. (August 2021, 2021 IEEE 17th International Conference on Automation Science and Engineering (CASE))

   A hybrid filtered basis function (FBF) approach is proposed in this paper for feedforward tracking control of linear systems with unmodeled nonlinear dynamics. Unlike most available tracking control techniques, the FBF approach is very versatile; it is applicable to any type of linear system, regardless of its underlying dynamics. The FBF approach expresses the control input to a system as a linear combination of basis functions with unknown coefficients. The basis functions are forward filtered through a linear model of the system's dynamics and the unknown coefficients are selected such that tracking error is minimized. The linear models used in existing implementations of the FBF approach are typically physics-based representations of the linear dynamics of a system. The proposed hybrid FBF approach expands the application of the FBF approach to systems with unmodeled nonlinearities by learning from data. A hybrid model is formulated by combining a physics-based model of the system's linear dynamics with a data-driven linear model that approximates the unmodeled nonlinear dynamics. The hybrid model is used online in receding horizon to compute optimal control commands that minimize tracking errors. The proposed hybrid FBF approach is shown in simulations on a model of a vibration-prone 3D printer to improve tracking accuracy by up to 65.4%, compared to an existing FBF approach that does not incorporate data. 

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2. Blind X-ray CT Image Reconstruction from Polychromatic Poisson Measurements

   https://doi.org/10.1109/TCI.2016.2523431  

   Gu, Renliang; Dogandzic, Aleksandar (February 2016, IEEE Transactions on Computational Imaging)

   We develop a framework for reconstructing images that are sparse in an appropriate transform domain from polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and incident-energy spectrum are unknown. Assuming that the object that we wish to reconstruct consists of a single material, we obtain a parsimonious measurement-model parameterization by changing the integral variable from photon energy to mass attenuation, which allows us to combine the variations brought by the unknown incident spectrum and mass attenuation into a single unknown mass-attenuation spectrum function; the resulting measurement equation has the Laplace-integral form. The mass-attenuation spectrum is then expanded into basis functions using B splines of order one. We consider a Poisson noise model and establish conditions for biconvexity of the corresponding negative log-likelihood (NLL) function with respect to the density-map and mass-attenuation spectrum parameters. We derive a block-coordinate descent algorithm for constrained minimization of a penalized NLL objective function, where penalty terms ensure nonnegativity of the mass-attenuation spline coefficients and nonnegativity and gradient-map sparsity of the density-map image, imposed using a convex total-variation (TV) norm; the resulting objective function is biconvex. This algorithm alternates between a Nesterov’s proximal-gradient (NPG) step and a limited-memory Broyden-Fletcher-Goldfarb-Shanno with box constraints (L-BFGS-B) iteration for updating the image and mass-attenuation spectrum parameters, respectively. We prove the Kurdyka-Łojasiewicz property of the objective function, which is important for establishing local convergence of block-coordinate descent schemes in biconvex optimization problems. Our framework applies to other NLLs and signal-sparsity penalties, such as lognormal NLL and ℓ₁ norm of 2D discrete wavelet transform (DWT) image coefficients. Numerical experiments with simulated and real X-ray CT data demonstrate the performance of the proposed scheme. 

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3. A Bayesian complex-valued latent variable model applied to functional magnetic resonance imaging

   https://doi.org/10.1093/jrsssc/qlae046  

   Sakitis, Chase_J; Brown, D_Andrew; Rowe, Daniel_B (September 2024, Journal of the Royal Statistical Society Series C: Applied Statistics)

   Abstract In linear regression, the coefficients are simple to estimate using the least squares method with a known design matrix for the observed measurements. However, real-world applications may encounter complications such as an unknown design matrix and complex-valued parameters. The design matrix can be estimated from prior information but can potentially cause an inverse problem when multiplying by the transpose as it is generally ill-conditioned. This can be combat by adding regularizers to the model but does not always mitigate the issues. Here, we propose our Bayesian approach to a complex-valued latent variable linear model with an application to functional magnetic resonance imaging (fMRI) image reconstruction. The complex-valued linear model and our Bayesian model are evaluated through extensive simulations and applied to experimental fMRI data. 

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4. Hierarchical Adaptive Loco-manipulation Control for Quadruped Robots

   https://doi.org/10.1109/ICRA48891.2023.10160523  

   Sombolestan, Mohsen; Nguyen, Quan (May 2023, IEEE)

   Legged robots have shown remarkable advantages in navigating uneven terrain. However, realizing effective loco-motion and manipulation tasks on quadruped robots is still challenging. In addition, object and terrain parameters are generally unknown to the robot in these problems. Therefore, this paper proposes a hierarchical adaptive control framework that enables legged robots to perform loco-manipulation tasks without any given assumption on the object's mass, the friction coefficient, or the slope of the terrain. In our approach, we first present an adaptive manipulation control to regulate the contact force to manipulate an unknown object on unknown terrain. We then introduce a unified model predictive control (MPC) for loco-manipulation that takes into account the manipulation force in our robot dynamics. The proposed MPC framework thus can effectively regulate the interaction force between the robot and the object while keeping the robot balance. Experimental validation of our proposed approach is successfully conducted on a Unitree A1 robot, allowing it to manipulate an unknown time-varying load up to 7 kg (60% of the robot's weight). Moreover, our framework enables fast adaptation to unknown slopes or different surfaces with different friction coefficients. 

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5. Robust Filtered Basis Functions Approach for Feedforward Tracking Control

   https://doi.org/10.1115/DSCC2018-9196  

   Ramani, Keval S.; Okwudire, Chinedum E. (September 2018, ASME 2018 Dynamic Systems and Control Conference)

   This paper proposes a robust filtered basis functions approach for feedforward tracking of linear time invariant systems with dynamic uncertainties. Identical to the standard filtered basis functions (FBF) approach, the robust FBF approach expresses the control trajectory as a linear combination of user-defined basis functions with unknown coefficients. The basis functions are forward filtered using a model of the plant and their coefficients are selected to minimize tracking errors. The standard FBF and robust FBF approaches differ in the filtering process. The robust FBF approach uses an optimal robust filter which is based on minimization of a frequency domain based error cost function over the dynamic uncertainty, whereas, the standard FBF approach uses the nominal model. Simulation examples and experiments on a desktop 3D printer are used to demonstrate significantly more accurate tracking of uncertain plants using robust FBF compared with the standard FBF. 

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