Related papers: Quantification of reachable attractors in asynchro…
We live in a world increasingly dominated by networks -- communications, social, information, biological etc. A central attribute of many of these networks is that they are dynamic, that is, they exhibit structural changes over time. While…
The majority of existing probabilistic model checking case studies are based on well understood theoretical models and distributions. However, real-life probabilistic systems usually involve distribution parameters whose values are obtained…
In this paper we propose augmented interval Markov chains (AIMCs): a generalisation of the familiar interval Markov chains (IMCs) where uncertain transition probabilities are in addition allowed to depend on one another. This new model…
In this paper a first order analytical system of difference equations is considered. For an asymptotically stable fixed point x0 of the system a gradual approximation of the domain of attraction DA is presented in the case when the matrix…
When designing optimal controllers for any system, it is often the case that the true state of the system is unknown to the controller, for example due to noisy measurements or partially observable states. Incomplete state information must…
In this paper the dynamics of an autonomous mathematical models of COVID-19 depending on a real parameter bifurcation, is controlled by switching periodically the parameter value. For this purpose the Parameter Switching (PS) algorithm is…
High dimensional random dynamical systems are ubiquitous, including -- but not limited to -- cyber-physical systems, daily return on different stocks of S&P 1500 and velocity profile of interacting particle systems around McKeanVlasov…
With the recent advent of a sound mathematical theory for extreme events in dynamical systems, new ways of analyzing a system's inherent properties have become available: Studying only the probabilities of extremely close Poincar\'{e}…
In this work, we propose a non-parametric technique for online modeling of systems with unknown nonlinear Lipschitz dynamics. The key idea is to successively utilize measurements to approximate the graph of the state-update function using…
We present an algorithm for data-driven reachability analysis that estimates finite-horizon forward reachable sets for general nonlinear systems using level sets of a certain class of polynomials known as Christoffel functions. The level…
Dynamic graph algorithms have seen significant theoretical advancements, but practical evaluations often lag behind. This work bridges the gap between theory and practice by engineering and empirically evaluating recently developed…
The climate is a complex non-equilibrium dynamical system that relaxes toward a steady state under the continuous input of solar radiation and dissipative mechanisms. The steady state is not necessarily unique. A useful tool to describe the…
In this paper, we study the reachability of two closely related matrices appearing in the analysis of linear time-varying (LTV) systems over a finite time interval, namely, its closed-loop state transition matrix via a state feedback…
In this paper, we study the robustness of safety properties of a linear dynamical system with respect to model uncertainties. Our paper involves three parts. In the first part, we provide symbolic (analytical) and numerical (representation…
Motivated by earlier work and the developer of a new algorithm, the FollowerStopper, this article uses reachability analysis to verify the safety of the FollowerStopper algorithm, which is a controller designed for dampening stop- and-go…
Multi-agent interacting systems are prevalent in the world, from pure physical systems to complicated social dynamic systems. In many applications, effective understanding of the situation and accurate trajectory prediction of interactive…
In quantum systems theory one of the fundamental problems boils down to: Given an initial state, which final states can be reached by the dynamic system in question? Formulated in the framework of bilinear control systems, the evolution…
Digital control has become increasingly prevalent in modern systems, making continuous-time plants controlled by discrete-time (digital) controllers ubiquitous and crucial across industries, including aerospace, automotive, and…
In this paper an autonomous analytical system of ordinary differential equations is considered. For an asymptotically stable steady state x0 of the system a gradual approximation of the domain of attraction DA is presented in the case when…
Complex networks have been found to provide a good representation of the structure of knowledge, as understood in terms of discoverable concepts and their relationships. In this context, the discovery process can be modeled as agents…