Related papers: Cross-Gramian-Based Combined State and Parameter R…
Model order reduction is a technique that is used to construct low-order approximations of large-scale dynamical systems. In this paper, we investigate a balancing based model order reduction method for dynamical systems with a linear…
Sparsity constraints on the control inputs of a linear dynamical system naturally arise in several practical applications such as networked control, computer vision, seismic signal processing, and cyber-physical systems. In this work, we…
We deduce a procedure to apply balanced truncation to parameter-dependent differential-algebraic systems. For that we solve multiple projected Lyapunov equations for different parameter values to compute the Gramians that are required for…
Observability quantification is a key problem in dynamic network sciences. While it has been thoroughly studied for linear systems, observability quantification for nonlinear networks is less intuitive and more cumbersome. One common…
Controllability and observability Gramians, along with their inverses, are widely used to solve various problems in control theory. This paper proposes spectral decompositions of the controllability Gramian and its inverse based on system…
In this work, the empirical-Gramian-based model reduction methods: Empirical poor man's truncated balanced realization, empirical approximate balancing, empirical dominant subspaces, empirical balanced truncation, and empirical balanced…
In this paper we show that inverses of well-conditioned, finite-time Gramians and impulse response matrices of large-scale interconnected systems described by sparse state-space models, can be approximated by sparse matrices. The…
This paper considers large-scale linear stochastic systems representing, e.g., spatially discretized stochastic partial differential equations. Since asymptotic stability can often not be ensured in such a stochastic setting (e.g. due to…
A key problem in process control is to decide which inputs should control which outputs. There are multiple ways to solve this problem, among them using gramian based measures, which include the Hankel interaction index array, the…
We discuss balanced truncation model order reduction for large-scale quadratic-bilinear (QB) systems. Balanced truncation for linear systems mainly involves the computation of the Gramians of the system, namely reachability and…
We propose a theoretical framework to study the eigenvalue spectra of the controllability Gramian of systems with random state matrices, such as networked systems with a random graph structure. Using random matrix theory, we provide…
This paper investigates the controllability of finite-dimensional linear fractional systems involving an uncertain parameter. We establish new results on the simultaneous and average controllability. In particular, we show that average…
Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…
We explain a method, inspired by control theory model reduction and interpolation theory, that rigorously establishes the types of coarse graining that are appropriate for systems with quadratic, generalized Hamiltonians. For such systems,…
This paper investigates the multitime linear normal PDE systems. We study especially the controllability of such systems, obtaining complementary results to those in our recent papers. Here the multitime controllability original results are…
While the optimization landscape of policy gradient methods has been recently investigated for partially observed linear systems in terms of both static output feedback and dynamical controllers, they only provide convergence guarantees to…
Many collective systems exist in nature far from equilibrium, ranging from cellular sheets up to flocks of birds. These systems reflect a form of active matter, whereby individual material components have internal energy. Under specific…
Cosmological probes pose an inverse problem where the measurement result is obtained through observations, and the objective is to infer values of model parameters which characterize the underlying physical system -- our Universe. Modern…
Dynamical systems with large state-spaces are often expensive to thoroughly explore experimentally. Coarse-graining methods aim to define simpler systems which are more amenable to analysis and exploration; most current methods, however,…
Given a linear dynamical system, we consider the problem of constructing an approximate system using only a subset of the sensors out of the total set such that the observability Gramian of the new system is approximately equal to that of…