Related papers: Invariants for Continuous Linear Dynamical Systems
The dynamics of many systems from physics, economics, chemistry, and biology can be modelled through polynomial functions. In this paper, we provide a computational means to find positively invariant sets of polynomial dynamical systems by…
This paper studies separating invariants: mappings on $D$ dimensional domains which are invariant to an appropriate group action, and which separate orbits. The motivation for this study comes from the usefulness of separating invariants in…
This paper assesses the transient stability of a synchronous machine connected to an infinite bus through the notion of invariant sets. The problem of computing a conservative approximation of the maximal positive invariant set is…
In this paper, we consider a control synthesis problem for a class of polynomial dynamical systems subject to bounded disturbances and with input constraints. More precisely, we aim at synthesizing at the same time a controller and an…
This paper focuses on the invariance control problem for discrete-time switched nonlinear systems. The proposed approach computes controlled invariant sets in a finite number of iterations and directly yields a partition-based invariance…
We revisit the classic problem of proving safety over parameterised concurrent systems, i.e., an infinite family of finite-state concurrent systems that are represented by some finite (symbolic) means. An example of such an infinite family…
The automatic generation of loop invariants is a fundamental challenge in software verification. While this task is undecidable in general, it is decidable for certain restricted classes of programs. This work focuses on invariant…
We propose to compute approximations to general invariant sets in dynamical systems by minimizing the distance between an appropriately selected finite set of points and its image under the dynamics. We demonstrate, through computational…
In this paper, we provide a direct data-driven approach to synthesize safety controllers for unknown linear systems affected by unknown-but-bounded disturbances, in which identifying the unknown model is not required. First, we propose a…
In this paper, we present a novel approach to synthesize invariant clusters for polynomial programs. An invariant cluster is a set of program invariants that share a common structure, which could, for example, be used to save the needs for…
A common technique for verifying the safety of complex systems is the inductive invariant method. Inductive invariants are inductive formulas that overapproximate the reachable states of a system and imply a desired safety property.…
The current paper is devoted to the investigation of the influence of nested invariant cone structure on the dynamics, in the context of non-autonomous (time almost periodic)cases. We first prove that the nested invariant cone structure can…
The investigation of nonlinear dynamical systems of the type $\dot{x}=P(x,y,z),\dot{y}=Q(x,y,z),\dot{z}=R(x,y,z)$ by means of reduction to some ordinary differential equations of the second order in the form…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
Time-invariant linear dynamical system arises in many real-world applications,and its usefulness is widely acknowledged. A practical limitation with this model is that its latent dimension that has a large impact on the model capability…
This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…
This paper presents a convex optimization-based framework for synthesizing time-varying controlled invariant funnels and associated feedback control around a given nominal trajectory for nonlinear systems subject to bounded disturbances.…
A central question in verification is characterizing when a system has invariants of a certain form, and then synthesizing them. We say a system has a $k$ linear invariant, $k$-LI in short, if it has a conjunction of $k$ linear (non-strict)…
In this paper, we propose an approach for computing invariant sets of discrete-time nonlinear systems by lifting the nonlinear dynamics into a higher dimensional linear model. In particular, we focus on the \emph{maximal admissible…
The Continuous Skolem Problem asks whether a real-valued function satisfying a linear differential equation has a zero in a given interval of real numbers. This is a fundamental reachability problem for continuous linear dynamical systems,…