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Data-driven approaches are increasingly popular for identifying dynamical systems due to improved accuracy and availability of sensor data. However, relying solely on data for identification does not guarantee that the identified systems will maintain their physical properties or that the predicted models will generalize well. In this paper, we propose a novel method for data-driven system identification by integrating a neural network as the first-order derivative of the learned dynamics in a Taylor series instead of learning the dynamical function directly. In addition, for dynamical systems with known monotonic properties, our approach can ensure monotonicity by constraining the neural network derivative to be non-positive or non-negative to the respective inputs, resulting in Monotonic Taylor Neural Networks (MTNN). Such constraints are enforced by either a specialized neural network architecture or regularization in the loss function for training. The proposed method demonstrates better performance compared to methods without the physics-based monotonicity constraints when tested on experimental data from an HVAC system and a temperature control testbed. Furthermore, MTNN shows good performance in a control application of a model predictive controller for a nonlinear MIMO system, illustrating the practical application of our method. 

Escherichia coli expresses surface appendages including fimbriae, flagella, and curli, at various levels in response to environmental conditions and external stimuli. Previous studies have revealed an interplay between expression of fimbriae and flagella in several E. coli strains, but how this regulation between fimbrial and flagellar expression affects adhesion to interfaces is incompletely understood. Here, we investigate how the concurrent expression of fimbriae and flagella by engineered strains of E. coli MG1655 affects their adhesion at liquid–solid and liquid–liquid interfaces. We tune fimbrial and flagellar expression on the cell surface through plasmid-based inducible expression of the fim operon and fliC-flhDC genes. We show that increased fimbrial expression increases interfacial adhesion as well as bacteria-driven actuation of micron-sized objects. Co-expression of flagella in fimbriated bacteria, however, does not greatly affect either of these properties. Together, these results suggest that interfacial adhesion as well as motion actuated by adherent bacteria can be altered by controlling the expression of surface appendages.