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The presence of global conserved quantities in interacting systems generically leads to diffusive transport at late times. Here, we show that systems conserving the dipole moment of an associated global charge, or even higher moment…
This work proposes a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations. The proposed…
We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…
In a dynamic network, the neighborhood of the vertices evolve across different temporal snapshots of the network. Accurate modeling of this temporal evolution can help solve complex tasks involving real-life social and interaction networks.…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…
In this paper we propose a model predictive control scheme for constrained fractional-order discrete-time systems. We prove that all constraints are satisfied at all time instants and we prescribe conditions for the origin to be an…
In this paper, we first establish an exponential stability result for a class of linear switched systems and then apply this result to show the existence of the distributed observer for a discrete-time leader system over jointly connected…
The paper studies the relation between a nonlinear time-varying flat discrete-time system and the corresponding linear time-varying systems which are obtained by a linearization along trajectories. It is motivated by the continuous-time…
We propose a computer-assisted approach to studying the effective continuum behavior of spatially discrete evolution equations. The advantage of the approach is that the "coarse model" (the continuum, effective equation) need not be…
Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time…
In this document the author proves that several problems in data-driven numerical approximation of dynamical systems in $\mathbb{C}^n$, can be reduced to the computation of a family of constrained matrix representations of elements of the…
We present a conservative/dissipative time integration scheme for nonlinear mechanical systems. Starting from a weak form, we derive algorithmic forces and velocities that guarantee the desired conservation/dissipation properties. Our…
Deep learning has made significant advances in creating efficient representations of time series data by automatically identifying complex patterns. However, these approaches lack interpretability, as the time series is transformed into a…
The objective of this paper is to study detectability, observability and related Lyapunov-type theorems of linear discrete-time time-varying stochastic systems with multiplicative noise. Some new concepts such as uniform detectability,…
While the design of optimal peak-to-peak controllers/observers for linear systems is known to be a difficult problem, this problem becomes interestingly much easier in the context of interval observers because of the positive nature of the…
A simply structured distributed observer is described for estimating the state of a discrete-time, jointly observable, input-free, linear system whose sensed outputs are distributed across a time-varying network. It is explained how to…
In this paper we propose an explicit two-level conservative scheme based on a TE/TM like splitting of the field components in time. Its dispersion properties are adjusted to accelerator problems. It is simpler and faster than the implicit…
In this contribution, we present a constructive method to derive flat sampled-data models for continuous-time flat systems through an implicit Euler-discretization. We show how the sampled-data model can be used subsequently for a…
We consider general infinite-dimensional dynamical systems with the Galilean and spatiotemporal scaling symmetry groups. Introducing the equivalence relation with respect to temporal scalings and Galilean transformations, we define a…