Related papers: Incremental Affine Abstraction of Nonlinear System…
In this paper, we consider the problem of piecewise affine abstraction of nonlinear systems, i.e., the overapproximation of its nonlinear dynamics by a pair of piecewise affine functions that "includes" the dynamical characteristics of the…
This paper proposes a method to compute finite abstractions that can be used for synthesizing robust hybrid control strategies for nonlinear systems. Most existing methods for computing finite abstractions utilize some global, analytical…
Predictive models are fundamental to engineering reliable software systems. However, designing conservative, computable approximations for the behavior of programs (static analyses) remains a difficult and error-prone process for modern…
We present abstract acceleration techniques for computing loop invariants for numerical programs with linear assignments and conditionals. Whereas abstract interpretation techniques typically over-approximate the set of reachable states…
PieceWise Affine (PWA) approximations for nonlinear functions have been extensively used for tractable, computationally efficient control of nonlinear systems. However, reaching a desired approximation accuracy without prior information…
We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced…
Abstract Interpretation approximates the semantics of a program by mimicking its concrete fixpoint computation on an abstract domain $\mathbb{A}$. The abstract (post-) fixpoint computation is classically divided into two phases: the…
How to effectively and reliably guarantee the correct functioning of safety-critical cyber-physical systems in uncertain conditions is a challenging problem. This paper presents a data-driven algorithm to derive approximate abstractions for…
Abstraction is essential for reducing the complexity of systems across diverse fields, yet designing effective abstraction methodology for probabilistic models is inherently challenging due to stochastic behaviors and uncertainties. Current…
This paper presents a compositional approach to specification-guided abstraction refinement for control synthesis of a nonlinear system associated with a method to over-approximate its reachable sets. Given an initial coarse partition of…
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be…
ASP programs are a convenient tool for problem solving, whereas with large problem instances the size of the state space can be prohibitive. We consider abstraction as a means of over-approximation and introduce a method to automatically…
We propose two novel numerical schemes for approximate implementation of the dynamic programming~(DP) operation concerned with finite-horizon, optimal control of discrete-time systems with input-affine dynamics. The proposed algorithms…
This paper presents an abstraction-refinement method to synthesize control inputs for a discrete-time piecewise linear system. The controlled system behavior satisfies a finite-word linear-time temporal objective while incurring minimal…
The von Neumann-Halperin method of alternating projections converges strongly to the projection of a given point onto the intersection of finitely many closed affine subspaces. We propose acceleration schemes making use of two ideas:…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Sufficiently accurate finite state models, also called symbolic models or discrete abstractions, allow one to apply fully automated methods, originally developed for purely discrete systems, to formally reason about continuous and hybrid…
In this paper, our aim is to propose a model for code abstraction, based on abstract interpretation, allowing us to improve the precision of a recently proposed static analysis by abstract interpretation of dynamic languages. The problem we…
This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence may exhibit instabilities similar to those of the base…
We consider the problem of under and over-approximating the image of general vector-valued functions over bounded sets, and apply the proposed solution to the estimation of reachable sets of uncertain non-linear discrete-time dynamical…