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We address in this paper the approximation problem of distributed delays. Such elements are convolution operators with kernel having bounded support, and appear in the control of time-delay systems. From the rich literature on this topic,…
Partial Differential Equations (PDEs) are fundamental tools for modeling physical phenomena, yet most PDEs of practical interest cannot be solved analytically and require numerical approximations. The feasibility of such numerical methods,…
For hybrid systems exhibiting periodic behavior, analyzing the invariant set containing the limit cycle is a natural way to study the robustness of the closed-loop system. However, computing these sets can be computationally expensive,…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
Hypergraph data, which capture multi-way interactions among entities, are increasingly prevalent in the big data era. Generating new hyperlinks from an observed, usually high-dimensional hypergraph is an important yet challenging task with…
In the scope of discrete finite-state models of interacting components, we present a novel algorithm for identifying sets of local states of components whose activity is necessary for the reachability of a given local state. If all the…
Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…
Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained…
The sequential compactness afforded hybrid systems under mild regularity constraints guarantee outer/upper semicontinuous dependence of solutions on initial conditions and perturbations. For reachable sets of hybrid systems, this property…
Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…
Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provide additional insight into underlying causative mechanisms.…
A neural ordinary differential equations network (ODE-Net)-enabled reachability method (Neuro-Reachability) is devised for the dynamic verification of networked microgrids (NMs) with unidentified subsystems and heterogeneous uncertainties.…
We propose novel less diffusive schemes for conservative one- and two-dimensional hyperbolic systems of nonlinear partial differential equations (PDEs). The main challenges in the development of accurate and robust numerical methods for the…
The propagation of primary discontinuities in initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Based on the (quasi-) Weierstra{\ss} form for regular matrix pencil, a complete characterization of…
Verification of discrete time or continuous time dynamical systems over the reals is known to be undecidable. It is however known that undecidability does not hold for various classes of systems: if robustness is defined as the fact that…
Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…
Time-delayed differential equations (TDDEs) are widely used to model complex dynamic systems where future states depend on past states with a delay. However, inferring the underlying TDDEs from observed data remains a challenging problem…
We discover restrained numerical instabilities in current training practices of deep networks with stochastic gradient descent (SGD), and its variants. We show numerical error (on the order of the smallest floating point bit and thus the…
Dyck reachability is the standard formulation of a large domain of static analyses, as it achieves the sweet spot between precision and efficiency, and has thus been studied extensively. Interleaved Dyck reachability (denoted $D_k\odot…
We present algorithms and their implementation to compute limit cycles and their isochrons for state-dependent delay equations (SDDE's) which are perturbed from a planar differential equation with a limit cycle. Note that the space of…