We study stability of multivariable control-affine nonlinear systems under sparsification of feedback controllers. Sparsification in our context refers to the scheduling of the individual control inputs one at a time in rapid periodic sweeps over the
set of control inputs, which corresponds to round-robin scheduling. We prove that if a locally asymptotically stabilizing feedback controller is sparsified via the round-robin scheme and each control action is scaled appropriately, then the corresponding equilibrium of the resulting system is stabilized when the scheduling is sufficiently fast; under mild additional conditions, local asymptotic stabilization of the corresponding equilibrium can also be guaranteed. Moreover, the basin of attraction for the equilibrium of scheduled system also remains same as the original system under sufficiently fast switching. Our technical tools are derived from optimal control theory, and our results also contribute to the literature on the stability of switched systems in the fast switching regime. Illustrative numerical examples depicting several subtle features of our results are included.
We study a constrained optimal control problem for an ensemble of control systems. Each sub-system (or plant) evolves on a matrix Lie group, and must satisfy given state and control action constraints pointwise in time. In addition, certain multiplex
ing requirement is imposed: the controller must be shared between the plants in the sense that at any time instant the control signal may be sent to only one plant. We provide first-order necessary conditions for optimality in the form of suitable Pontryagin maximum principle in this problem. Detailed numerical experiments are presented for a system of two satellites performing energy optimal maneuvers under the preceding family of constraints.
Next generation batteries based on lithium (Li) metal anodes have been plagued by the dendritic electrodeposition of Li metal on the anode during cycling, resulting in short circuit and capacity loss. Suppression of dendritic growth through the use o
f solid electrolytes has emerged as one of the most promising strategies for enabling the use of Li metal anodes. We perform a computational screening of over 12,000 inorganic solids based on their ability to suppress dendrite initiation in contact with Li metal anode. Properties for mechanically isotropic and anisotropic interfaces that can be used in stability criteria for determining the propensity of dendrite initiation are usually obtained from computationally expensive first-principles methods. In order to obtain a large dataset for screening, we use machine learning models to predict the mechanical properties of several new solid electrolytes. We train a convolutional neural network on the shear and bulk moduli purely on structural features of the material. We use AdaBoost, Lasso and Bayesian ridge regression to train the elastic constants, where the choice of the model depended on the size of the training data and the noise that it can handle. Our models give us direct interpretability by revealing the dominant structural features affecting the elastic constants. The stiffness is found to increase with a decrease in volume per atom, increase in minimum anion-anion separation, and increase in sublattice (all but Li) packing fraction. Cross-validation/test performance suggests our models generalize well. We predict over 20 mechanically anisotropic interfaces between Li metal and 6 solid electrolytes which can be used to suppress dendrite growth. Our screened candidates are generally soft and highly anisotropic, and present opportunities for simultaneously obtaining dendrite suppression and high ionic conductivity in solid electrolytes.
