Related papers: Invariant Funnels around Trajectories using Sum-of…
We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems…
We consider space-saving versions of several important operations on univariate polynomials, namely power series inversion and division, division with remainder, multi-point evaluation, and interpolation. Now-classical results show that…
We study optimization-based criteria for the stability of switching systems, known as Path-Complete Lyapunov Functions, and ask the question "can we decide algorithmically when a criterion is less conservative than another". Our…
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 new algorithm is presented to find exact traveling wave solutions of differential-difference equations in terms of tanh functions. For systems with parameters, the algorithm determines the conditions on the parameters so that the…
In this work, we develop a localized numerical scheme with low regularity requirements for solving time-fractional integro-differential equations. First, a fully discrete numerical scheme is constructed. Specifically, for temporal…
Automatically generating invariants, key to computer-aided analysis of probabilistic and deterministic programs and compiler optimisation, is a challenging open problem. Whilst the problem is in general undecidable, the goal is settled for…
We propose an approach to determine the continual progression of algorithmic efficiency, as an alternative to standard calculations of time complexity, likely, but not exclusively, when dealing with data structures with unknown maximum…
Functional digraphs are unlabelled finite digraphs where each vertex has exactly one out-neighbor. They are isomorphic classes of finite discrete-time dynamical systems. Endowed with the direct sum and product, functional digraphs form a…
This paper investigates how to recover parameters of a linear time invariant system from values and derivatives of its transfer function matrix, along several particular directions at a prescribed set of points in the complex plane, in…
In order to analyze structure of tangent spaces of a transient orbit, we propose a new algorithm which pulls back vectors in tangent spaces along the orbit by using a calculation method of covariant Lyapunov vectors. As an example, the…
This paper presents an automated algorithm to analyze the stability of piecewise affine (PWA) dynamical systems due to their broad applications. We parametrize the Lyapunov function as a PWA function, with polytopic regions defined by the…
Simulation-based verification algorithms can provide formal safety guarantees for nonlinear and hybrid systems. The previous algorithms rely on user provided model annotations called discrepancy function, which are crucial for computing…
This article focuses on automatically generating polynomial equations that are inductive loop invariants of computer programs. We propose a new algorithm for this task, which is based on polynomial interpolation. Though the proposed…
We propose an iterative algorithm for the numerical computation of sums of squares of polynomials approximating given data at prescribed interpolation points. The method is based on the definition of a convex functional $G$ arising from the…
Automatically generating invariants, key to computer-aided analysis of probabilistic and deterministic programs and compiler optimisation, is a challenging open problem. Whilst the problem is in general undecidable, the goal is settled for…
We present a novel method to compute componentwise transient bounds, ultimate bounds, and invariant regions for a class of switching continuous-time linear systems with perturbation bounds that may depend nonlinearly on a delayed state. The…
Symmetry in differential equations reveals invariances and offers a powerful means to reduce model complexity. Lie group analysis characterizes these symmetries through infinitesimal generators, which provide a local, linear criterion for…
The joint spectral radius (JSR) of a set of matrices characterizes the maximal asymptotic growth rate of an infinite product of matrices of the set. This quantity appears in a number of applications including the stability of switched and…
Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials. These include: tightly containing a cloud of points (e.g., representing an…