Stabilizing dynamical systems in science and engineering is challenging, especially in edge cases and limit states where typically little data are available. In this work, we propose a data-driven approach that guarantees finding stabilizing controllers from as few data samples as the dimension of the unstable dynamics, which typically is orders of magnitude lower than the state dimension of...
We consider a vibrational system control problem over a finite time horizon. The performance measure of the system is taken to be $p$-mixed $H_2$ norm which generalizes the standard $H_2$ norm. We present an algorithm for efficient calculation of this norm in the case when the system is parameter dependent and the number of inputs or outputs of the system is significantly smaller than the...
We consider the mathematical model of a low orbit satellite with electromagnetic actuation described in the recent paper [R.Misra,R.Wisniewski, A.Z. ”Attitude Stabilization of a Satellite having only Electromagnetic Actuation using Oscillating Controls”, Aerospace (submitted)]. This model is not fully actuated as the control torque is proportional to the vector product of the geomagnetic field...
Type 1 diabetes (T1D) is a chronic disease caused by autoimmune desctruction of the pancreatic insulin-producing cells. People with T1D spend significant amounts of time on self-treatment with insulin infusion or injections. However, this task is non-trivial, and administering too much insulin can be dangerous. Conversely, administering too little insulin for longer periods of time can lead to...
We consider the Riemannian submanifold of matrix-valued rational functions of fixed McMillan degree embedded in the Hardy $\mathcal{H}_2$ space and explore whether IRKA can be interpreted as a Riemannian optimization method over this manifold.
We study a posteriori error estimation and adaptivity with the goal of automatic model order reduction of large-scale systems. We propose efficient offline adaptive techniques that are aimed at (a) bringing down the significant offline cost often associated with generating reduced-order models and (b) minimizing the user interference in obtaining efficient reduced-order models. Adaptivity is...
Simulating dynamics of deforming surfaces is very expensive, particularly when internal forces, acting on vertices and/or their connecting faces, require real-time update, and especially because the 2-dimensional objects embedded in 3D spaces are meshes with hundreds of thousands of vertices. The dynamical behavior of such structure is governed by Newton's law of motion for mechanical systems...
Centrality measures identify and rank the most influential entities of complex networks. In this talk, we generalize matrix function-based centrality measures, which have been studied extensively for single-layer and temporal networks in recent years to layer-coupled multiplex networks. The layers of these networks can reflect different relationships and interactions between entities or...
Dynamical modeling of a process is essential to study its dynamical behavior and perform engineering studies such as control and optimization. With the ease of accessibility of data, learning models directly from the data have recently drawn much attention. It is also desirable to construct simple and compact models describing complex nonlinear high-fidelity dynamics for efficient simulations...
