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This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…
This paper proposes a tractable framework to determine key characteristics of non-linear dynamic systems by converting physics-informed neural networks to a mixed integer linear program. Our focus is on power system applications.…
We present an algorithm for finding the probabilities of rare events in nonequilibrium processes. The algorithm consists of evolving the system with a modified dynamics for which the required event occurs more frequently. By keeping track…
Artificial neural networks, widely recognised for their role in machine learning, are now transforming the study of ordinary differential equations (ODEs), bridging data-driven modelling with classical dynamical systems and enabling the…
We investigate the stability properties of discrete and hybrid stochastic nonlinear dynamical systems. More precisely, we extend the stochastic contraction theorems (which were formulated for continuous systems) to the case of discrete and…
Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous…
Learning models of dynamical systems characterized by specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems and stability…
End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…
We consider the problem of designing robust state-feedback controllers for discrete-time linear time-invariant systems, based directly on measured data. The proposed design procedures require no model knowledge, but only a single open-loop…
A resilient multi-vehicle system cooperatively performs tasks by exchanging information, detecting, and removing cyber attacks that have the intent of hijacking or diminishing performance of the entire system. In this paper, we propose a…
Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…
We consider a model for substrate-depletion oscillations in genetic systems, based on a stochastic differential equation with a slowly evolving external signal. We show the existence of critical transitions in the system. We apply two…
The main task in analyzing a switching network design (including circuit-, multirate-, and photonic-switching) is to determine the minimum number of some switching components so that the design is non-blocking in some sense (e.g., strict-…
We consider optimization algorithms that are open systems, that is, with external inputs and outputs. Such algorithms arise for instance, when analyzing the effect of noise or disturbance on an algorithm, or when an algorithm is part of…
This Survey provides an overview of techniques in termination analysis for programs with numerical variables and transitions defined by linear constraints. This subarea of program analysis is challenging due to the existence of undecidable…
A finite-element discretization of such an equation yields a linear system whose conditioning worsens as the variations in the values of PDE coefficients becomes large. This paper introduces a procedure by which the discrete system obtained…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
A new framework is developed for control of constrained nonlinear systems with structured parametric uncertainties. Forward invariance of a safe set is achieved through online parameter adaptation and data-driven model estimation. The new…
Quantum computing allows for the manipulation of highly correlated states whose properties quickly go beyond the capacity of any classical method to calculate. Thus one natural problem which could lend itself to quantum advantage is the…
The increasing uncertainty in modern power systems, driven by the integration of intermittent energy sources and variable loads, underscores the need for probabilistic transient stability assessment. However, existing assessment methods…