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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. Weak and strong solutions for a fluid‐poroelastic‐structure interaction via a semigroup approach

   https://doi.org/10.1002/mma.10533  

   Avalos, George; Gurvich, Elena; Webster, Justin_T (October 2024, Mathematical Methods in the Applied Sciences)

   A filtration system comprising a Biot poroelastic solid coupled to an incompressible Stokes free‐flow is considered in 3D. Across the flat 2D interface, the Beavers‐Joseph‐Saffman coupling conditions are taken. In the inertial, linear, and non‐degenerate case, the hyperbolic‐parabolic coupled problem is posed through a dynamics operator on a chosen energy space, adapted from Stokes‐Lamé coupled dynamics. A semigroup approach is utilized to circumvent issues associated to mismatched trace regularities at the interface. The generation of a strongly continuous semigroup for the dynamics operator is obtained via a non‐standard maximality argument. The latter employs a mixed‐variational formulation in order to invoke the Babuška‐Brezzi theorem. The Lumer‐Philips theorem then yields semigroup generation, and thereby, strong and generalized solutions are obtained. For the linear dynamics, density obtains the existence of weak solutions; we extend to the case where the Biot compressibility of constituents degenerates. Thus, for the inertial linear Biot‐Stokes filtration system, we provide a clear elucidation of strong solutions and a construction of weak solutions, as well as their regularity through associated estimates. 

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3. Signatures of coherent vibrational dynamics in ethylene carbonate

   https://doi.org/10.1063/5.0216515  

   Guerrieri, Luke; Hall, Sarah; Luther, Brad M; Krummel, Amber T (October 2024, The Journal of Chemical Physics)

   Lian, Tianquan (Ed.)

   Despite having practical applications in battery technology and serving as a model system for Fermi resonance coupling, ethylene carbonate (EC) receives little direct attention as a vibrational probe in nonlinear vibrational spectroscopy experiments. EC contains a Fermi resonance that is well-characterized in the linear spectrum, and the environmental sensitivity of its Fermi resonance peaks could make it a good molecular probe for two-dimensional infrared spectroscopy (2DIR) experiments. As a model system, we investigate the linear and 2DIR vibrational spectrum of the carbonyl stretching region of ethylene carbonate in tetrahydrofuran. The 2DIR spectrum reveals peak dynamics that evolve coherently. We characterize these dynamics in the context of Redfield theory and find evidence that EC dynamics proceed through coherent pathways, including singular coherence transfer pathways that have not been widely observed in other studies. We find that coherent contributions play a significant role in the observed dynamics of cross-peaks in the 2DIR spectrum, which must be accounted for to extract accurate measurements of early waiting time dynamics. 

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4. Robustness guarantees for structured model reduction of dynamical systems with applications to biomolecular models

   https://doi.org/10.1002/rnc.6013  

   Pandey, Ayush; Murray, Richard M. (January 2022, International Journal of Robust and Nonlinear Control)

   Abstract Model reduction methods usually focus on the error performance analysis; however, in presence of uncertainties, it is important to analyze the robustness properties of the error in model reduction as well. This problem is particularly relevant for engineered biological systems that need to function in a largely unknown and uncertain environment. We give robustness guarantees for structured model reduction of linear and nonlinear dynamical systems under parametric uncertainties. We consider a model reduction problem where the states in the reduced model are a strict subset of the states of the full model, and the dynamics for all of the other states are collapsed to zero (similar to quasi‐steady‐state approximation). We show two approaches to compute a robustness guarantee metric for any such model reduction—a direct linear analysis method for linear dynamics and a sensitivity analysis based approach that also works for nonlinear dynamics. Using the robustness guarantees with an error metric and an input‐output mapping metric, we propose an automated model reduction method to determine the best possible reduced model for a given detailed system model. We apply our method for the (1) design space exploration of a gene expression system that leads to a new mathematical model that accounts for the limited resources in the system and (2) model reduction of a population control circuit in bacterial cells. 

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5. Polariton spectra under the collective coupling regime. I. Efficient simulation of linear spectra and quantum dynamics

   https://doi.org/10.1063/5.0243535  

   Mondal, M Elious; Vamivakas, A Nickolas; Cundiff, Steven T; Krauss, Todd D; Huo, Pengfei (January 2025, The Journal of Chemical Physics)

   We outline two general theoretical techniques to simulate polariton quantum dynamics and optical spectra under the collective coupling regimes described by a Holstein–Tavis–Cummings (HTC) model Hamiltonian. The first one takes advantage of sparsity of the HTC Hamiltonian, which allows one to reduce the cost of acting polariton Hamiltonian onto a state vector to the linear order of the number of states, instead of the quadratic order. The second one is applying the well-known Chebyshev series expansion approach for quantum dynamics propagation and to simulate the polariton dynamics in the HTC system; this approach allows us to use a much larger time step for propagation and only requires a few recursive operations of the polariton Hamiltonian acting on state vectors. These two theoretical approaches are general and can be applied to any trajectory-based non-adiabatic quantum dynamics methods. We apply these two techniques with our previously developed Lindblad-partially linearized density matrix approach to simulate the linear absorption spectra of the HTC model system, with both inhomogeneous site energy disorders and dipolar orientational disorders. Our numerical results agree well with the previous analytic and numerical work. 

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