## About

76

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504

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Citations since 2017

Introduction

Homepage: http://lcs.ios.ac.cn/~xuebai/index.html

**Skills and Expertise**

Additional affiliations

November 2015 - October 2017

May 2014 - October 2015

September 2008 - January 2014

## Publications

Publications (76)

In this paper we propose a set-boundary based method to verify reach-avoid properties of non-linear dynamical systems with parametric uncertainty, which works under the assumption that the initial set is a compact set. In comparison to the conventional approach employing safely overapproximating state extrapolation on the full volume of the initial...

Delay differential equations (DDEs) play an important role in the modeling of dynamic processes. Delays may arise in contemporary control schemes like networked distributed control and may cause deterioration of control performance, invalidating both stability and safety properties. This induces an interest in DDE especially in the area of modeling...

Under-approximations are useful for falsification of safety properties for nonlinear (hybrid) systems by finding counter-examples. Polytopic under-approximations enable analysis of these properties using reasoning in the theory of linear arithmetic.
Given a nonlinear system, a target region of the simply connected compact type and a time duration,...

In this paper we study reachability verification problems of stochastic discrete-time dynamical systems over the infinite time horizon. The reachability verification of interest in this paper is to certify specified lower and upper bounds of the reachability probability, with which the system starting from a designated initial set will enter a desi...

Reach-avoid analysis combines the construction of safety and specific progress guarantees, and is able to formalize many important engineering problems. In this paper we study the reach-avoid verification problem of systems modelled by ordinary differential equations using Lyapunov densities. Firstly, the weak reach-avoid verification is considered...

Credit assignment problem of neural networks refers to evaluating the credit of each network component to the final outputs. For an untrained neural network, approaches to tackling it have made great contributions to parameter update and model revolution during the training phase. This problem on trained neural networks receives rare attention, nev...

Neural networks (NNs) are increasingly applied in safety-critical systems such as autonomous vehicles. However, they are fragile and are often ill-behaved. Consequently, their behaviors should undergo rigorous guarantees before deployment in practice. In this paper we propose a set-boundary reachability method to investigate the safety verification...

A barrier certificate often serves as an inductive invariant that isolates an unsafe region from the reachable set of states, and hence is widely used in proving safety of hybrid systems possibly over an infinite time horizon. We present a novel condition on barrier certificates, termed the invariant barrier-certificate condition, that witnesses un...

A barrier certificate often serves as an inductive invariant that isolates an unsafe region from the reachable set of states, and hence is widely used in proving safety of hybrid systems possibly over an infinite time horizon. We present a novel condition on barrier certificates, termed the invariant barrier-certificate condition, that witnesses un...

In this paper we propose a novel semi-definite programming approach that solves reach-avoid problems over open (i.e., not bounded a priori) time horizons for dynamical systems modeled by polynomial stochastic differential equations. The reach-avoid problem in this paper is a probabilistic guarantee: we approximate from the inner a p-reach-avoid set...

In this paper we propose novel optimization-based methods for verifying reach-avoid (or, eventuality) properties of continuous-time systems modelled by ordinary differential equations. Given a system, an initial set, a safe set and a target set of states, we say that the reach-avoid property holds if for all initial conditions in the initial set, a...

This letter is to investigate the stability verification for heterogeneous polynomial complex networks through iterative sum-of-squares programming approach. With polynomial Lyapunov functions, a global asymptotic stability criterion is established for the heterogeneous complex networks under the directed topology. Based on the proposed criterion,...

Reach-avoid analysis, which involves the computation of reach-avoid sets, is an established tool that provides hard guarantees of safety (via avoiding unsafe states) and target reachability (via reaching target sets), and therefore is widely used in safe-critical systems design such as air traffic management systems and biomedical systems. This pap...

A barrier certificate often serves as an inductive invariant that isolates an unsafe region from the reachable set of states, and hence is widely used in proving safety of hybrid systems possibly over the infinite time horizon. We present a novel condition on barrier certificates, termed the invariant barrier-certificate condition, that witnesses u...

In this paper, we propose a framework of filter-based ensemble of deep neuralnetworks (DNNs) to defend against adversarial attacks. The framework builds an ensemble of sub-models -- DNNs with differentiated preprocessing filters. From the theoretical perspective of DNN robustness, we argue that under the assumption of high quality of the filters, t...

A barrier certificate often serves as an inductive invariant that isolates an unsafe region from the reachable set of states, and hence is widely used in proving safety of hybrid systems possibly over the infinite time horizon. We present a novel condition on barrier certificates, termed the invariant barrier-certificate condition, that witnesses u...

This article investigates the consensus tracking problem of the heterogeneous multivehicle systems (MVSs) under a repeatable control environment. First, a unified iterative learning control (ILC) algorithm is presented for all autonomous vehicles, each of which is governed by both discrete- and continuous-time nonlinear dynamics. Then, several cons...

Delays are ubiquitous in modern hybrid systems, which exhibit both continuous and discrete dynamical behaviors. Induced by signal transmission, conversion, the nature of plants, and so on, delays may appear either in the continuous evolution of a hybrid system such that the evolution depends not only on the present state but also on its execution h...

We propose a spurious region guided refinement approach for robustness verification of deep neural networks. Our method starts with applying the DeepPoly abstract domain to analyze the network. If the robustness property cannot be verified, the result is inconclusive. Due to the over-approximation, the computed region in the abstraction may be spur...

In this paper we study the maximal robust invariant set estimation problem for discrete-time perturbed nonlinear systems within the optimal control framework. The maximal robust invariant set of interest is a set of all states such that every possible trajectory starting from it never violates a specified state constraint, regardless of actual dist...

Stochastic discrete-time systems, i.e., discrete-time dynamic systems subject to stochastic disturbances, are an essential modelling tool for many engineering systems, and reach-avoid analysis is able to guarantee safety (i.e., via avoiding unsafe sets) and performance (i.e., via reaching target sets). In this paper we study the infinite time reach...

This paper proposes a black box based approach for analysing deep neural networks (DNNs). We view a DNN as a function $\boldsymbol{f}$ from inputs to outputs, and consider the local robustness property for a given input. Based on scenario optimization technique in robust control design, we learn the score difference function $f_i-f_\ell$ with respe...

We study the problem of learning deterministic one-clock timed automata in the framework of PAC (probably approximately correct) learning. The use of PAC learning relaxes the assumption of having a teacher that can answer equivalence queries exactly, replacing it with approximate answers from testing on a set of samples. The framework provides corr...

In this paper we propose a novel semi-definite programming based method to compute
robust domains of attraction for state-constrained perturbed polynomial systems. A robust domain
of attraction is a set of states such that every trajectory starting from it will approach an equilibrium
while never violating a specified state constraint, regardless o...

In this paper we propose a novel semi-definite programming based method to compute
robust domains of attraction for state-constrained perturbed polynomial systems. A robust domain of attraction is a set of states such that every trajectory starting from it will approach an equilibrium while never violating a specified state constraint, regardless o...

In this paper we propose a computational method based on semi-definite programming for synthesizing infinite-time reach-avoid sets in discrete-time polynomial systems. An infinite-time reach-avoid set is a set of initial states making the system eventually, i.e., within finite time enter the target set while remaining inside another specified (safe...

In this paper we propose a linear programming based method to generate interpolants for two Boolean formulas in the framework of probably approximately correct (PAC) learning. The computed interpolant is termed as a PAC interpolant with respect to a violation level \(\epsilon \in (0,1)\) and confidence level \(\beta \in (0,1)\): with at least \(1-\...

We propose a spurious region guided refinement approach for robustness verification of deep neural networks. Our method starts with applying the DeepPoly abstract domain to analyze the network. If the robustness property cannot be verified, the result is inconclusive. Due to the over-approximation, the computed region in the abstraction may be spur...

In this paper we propose a convex programming based method for computing robust regions of attraction for state-constrained perturbed discrete-time polynomial systems. The robust region of attraction of interest is a set of states such that every possible trajectory initialized in it will approach an equilibrium state while never violating the spec...

In this paper we present a novel model checking approach to finite-time safety verification of black-box continuous-time dynamical systems within the framework of probably approximately correct (PAC) learning. The black-box dynamical systems are the ones, for which no model is given but whose states changing continuously through time within a finit...

Random ordinary differential equations (RODEs) are ordinary differential equations (ODEs) that contain a stochastic process in their vector field functions. They have been used for many years in a wide range of applications, but have been a shadow existence to stochastic differential equations (SDEs) despite being able to model a wider and often ph...

In this paper we present a novel model checking approach to finite-time safety verification of black-box continuous-time dynamical systems within the framework of probably approximately correct (PAC) learning. The black-box dynamical systems are the ones, for which no model is given but whose states changing continuously through time within a finit...

In this paper, we propose a method for bounding the probability that a stochastic differential equation (SDE) system violates a safety specification over the infinite time horizon. SDEs are mathematical models of stochastic processes that capture how states evolve continuously in time. They are widely used in numerous applications such as engineere...

Craig interpolant generation for non-linear theory and its combination with other theories are still in infancy, although interpolation-based techniques have become popular in the verification of programs and hybrid systems where non-linear expressions are very common. In this paper, we first prove that a polynomial interpolant of the form \(h(\mat...

In this paper we present a Bellman equation for computing robust regions of attraction for state-constrained perturbed discrete-time systems. The robust region of attraction of interest is a set of states such that every trajectory initialized in it will approach an equilibrium while never violating the specified state constraint, regardless of the...

In this paper, we propose a method for bounding the probability that a stochastic differential equation (SDE) system violates a safety specification over the infinite time horizon. SDEs are mathematical models of stochastic processes that capture how states evolve continuously in time. They are widely used in numerous applications such as engineere...

This note explores reach set computations for perturbed delay differential equations (DDEs). The perturbed DDEs of interest in this note is a class of DDEs whose dynamics are subject to perturbations, and their solutions feature the local homeomorphism property with respect to initial states. Membership in this class of perturbed DDEs is determined...

This article explores reachable set computations for a class of delay differential equations(DDEs), in which dynamics of the DDE are perturbed and the DDE driven by each perturbation input exhibits solutions featuring local homeomorphism property with respect to initial states. Membership in this class of perturbed DDEs is determined by conducting...

In this paper we propose a convex programming based method for computing robust regions of attraction for state-constrained perturbed discrete-time polynomial systems. The robust region of attraction of interest is a set of states such that every possible trajectory initialized in it will approach an equilibrium state while never violating the spec...

In this paper we present a Bellman equation for computing robust regions of attraction for state-constrained perturbed discrete-time systems. The robust region of attraction of interest is a set of states such that every trajectory initialized in it will approach an equilibrium while never violating a specified state constraint, regardless of the a...

In this paper we present a method based on linear programming that facilitates reliable safety verification of hybrid dynamical systems subject to perturbation inputs over the infinite time horizon. The verification algorithm applies the probably approximately correct (PAC) learning framework and consequently can be regarded as statistically formal...

Dear Colleagues,
I write to you in my role as the Asian publicity chair for ICCPS 2020 (http://iccps.acm.org/2020/). I would like to invite you and/or your colleagues to submit an Original Research Article to ICCPS 2020.
ACM/IEEE ICCPS is the premier single-track conference for reporting advances in all CPS aspects, including theory, tools, appl...

Given a family of independent and identically distributed samples extracted from the input region and their corresponding outputs, in this paper we propose a method to under-approximate the set of safe inputs that lead the black-box system to respect a given safety specification. Our method falls within the framework of probably approximately corre...

In this paper we present a method based on linear programming that facilitates reliable safety verification of hybrid dynamical systems over the infinite time horizon subject to perturbation inputs. The verification algorithm applies the probably approximately correct (PAC) learning framework and consequently can be regarded as statistically formal...

Delayed coupling between state variables occurs regularly in technical dynamical systems, especially embedded control. As it consequently is omnipresent in safety-critical domains, there is an increasing interest in the safety verification of systems modelled by Delay Differential Equations (DDEs). In this paper, we leverage qualitative guarantees...

Invariant generation plays a central role in the verification of programs and hybrid systems. In this paper, we propose an approach to synthesize invariants using semidefinite programming (SDP) that combine advantages of both symbolic constraint solving and numeric constraint solving. The advantages of our approach is threefold: first, it is powerf...

Interpolation-based techniques have become popularized in recent years because of their inherently modular and local reasoning, which can scale up existing formal verification techniques like theorem proving, model-checking, abstraction interpretation, and so on, while the scalability is the bottleneck of these techniques. Craig interpolant generat...

In this paper we study the problem of computing robust invariant sets for state-constrained perturbed polynomial systems within the Hamilton-Jacobi reachability framework. A robust invariant set is a set of states such that every possible trajectory starting from it never violates the given state constraint, irrespective of the actual perturbation....

Delayed coupling between state variables occurs regularly in technical dynamical systems, especially embedded control. As it consequently is omnipresent in safety-critical domains, there is an increasing interest in the safety verification of systems modelled by Delay Differential Equations (DDEs). In this paper, we leverage qualitative guarantees...

In this paper we systematically study the problem of computing robust invariant sets for switched discrete-time polynomial systems subject to state constraints from theoretical and computational perspectives.\footnote{A switched system is defined by a family of subsystems and a switching rule orchestrating the switching between subsystems.} A robus...

Reach-avoid differential games play an important role in collision avoidance, motion planning and control of aircrafts, and related applications. The central problem is the computation of the set of initial states from which the ego player can enforce the satisfiability of safety specifications over a specified time horizon. Previous methods addres...

In this paper we propose a convex programming based method to address a long-standing problem of inner-approximating
backward reachable sets of state-constrained polynomial systems subject to time-varying uncertainties. The backward reachable set
is a set of states, from which all trajectories starting will surely enter a target region at the end o...

In this paper we propose a convex programming based method for computing robust regions of attraction for state-constrained perturbed discrete-time polynomial systems. The robust region of attraction of interest is a set of states such that every possible trajectory initialized in it will approach an equilibrium state while never violating the spec...

Numerical software is widely used in safety-critical systems such as aircrafts, satellites, car engines and many other fields, facilitating dynamics control of such systems in real time. It is therefore absolutely necessary to verify their correctness. Most of these verifications are conducted under ideal mathematical models, but their real executi...

In this paper we suggest a method based on convex programming for computing semi-algebraic under-approximations of reach sets for polynomial continuous systems with initial sets being the zero sub-level set of a polynomial function. It is well-known that the reachable set can be formulated as the zero sub-level set of a value function to a Hamilton...

Numerical software are widely used in safety-critical systems such as aircrafts, satellites, car engines and so on, facilitating dynamics control of such systems in real time, it is therefore absolutely necessary to verify their correctness. It is a long standing challenge to guarantee verified properties of numerical software are indeed satisfied...

We suggest a method for significantly reducing the so-called
wrapping effect, i.e., the accumulation of approximation errors
incurred during reach-set computation of differential equations when
repeatedly over-approximating intermediate reach sets by tractable
computational representations of sets in the $\Real^n$. Our method
can be implemented on...

Delays in feedback control loop, as induced by networked distributed control schemes, may have detrimental effects on control performance. This induces an interest in safety verification of delay differential equations (DDEs) used as a model of embedded control. This article explores reachable-set computation for a class of DDEs featuring a local h...

Delay differential equations (DDEs) play an important role in the modeling of dynamic processes. Delays arise in contemporary control schemes like networked distributed control and can cause deterioration of control performance, invalidating both stability and safety properties. This induces an interest in DDE especially in the area of modeling and...

Under-approximations of backward reachable sets play an important role in controller synthesis and trajectory analysis for constrained nonlinear dynamical systems, but there are few methods available to compute them. Given a nonlinear system, a target region of simply connected compact type and a time duration, we present a method using boundary an...

We in this paper analyze the global exponential stability of switched hybrid systems, whose subsystems have polynomial vector fields, by discovering multiple Lyapunov functions in quadratic forms. We start with an algebraizable sufficient condition for the existence of quadratic multiple Lyapunov functions. Then, since different discrete modes are...

In this paper we analyze local asymptotic stability of switched hybrid systems, whose subsystems have polynomial vector fields, by discovering multiple Lyapunov functions in quadratic forms. We start with an algebraizable sufficient condition for the existence of quadratic multiple Lyapunov functions. Then, since different discrete modes are consid...

In this paper we analyze locally asymptotic stability of polynomial dynamical systems by discovering local Lyapunov functions beyond quadratic forms. We first derive an algebraizable sufficient condition for the existence of a polynomial Lyapunov function. Then we apply a real root classification based method step by step to under-approximate this...

Reachability analysis and viability theory play an important role in control synthesis and trajectory analysis of constrained dynamical systems, many methods are known for computing them in low-dimensional non-linear systems, but these well-known methods rely on gridding the state space and hence suffer from the curse of dimensionality. In this stu...

In this paper we propose a mechanisable approach for discovering multiple Lyapunov functions for switched hybrid systems. We start with the classical definition on asymptotic stability, which can be assured by the existence of multiple Lyapunov functions. Then, we derive an algebraizable sufficient condition on multiple Lyapunov functions in quadra...

In this paper, we present a sum of squares programming based method for computing a basin of attraction to a target region as large as possible by iteratively searching for Lyapunov-like functions. We start with the basic mathematical notions and show how attraction to a target region can be ensured by Lyapunov-like functions. Then, we present an i...

In this paper we propose a mechanisable technique for asymptotic stability analysis of continuous dynamical systems. We start from linearizing a continuous dynamical system, solving the Lyapunov matrix equation and then check whether the solution is positive definite. For the cases that the Jacobian matrix is not a Hurwitz matrix, we first derive a...

## Projects

Projects (3)

With the rapid development of feedback control, sensor techniques and computer control, time delays have become an essential feature that may well annihilate the safety certificate and control performance of embedded systems. This project aims to rigorously verify and design reliable safety-critical cyber-physical systems involving time delays, which often yield substantially higher theoretical complexity in contrast to delay-free systems.