This work is concerned with the safety controller synthesis of stochastic hybrid systems, in which continuous evolutions are described by stochastic differential equations with both Brownian motions and Poisson processes, and instantaneous jumps are governed by stochastic difference equations with additive noises. Our proposed framework leverages the notion of control barrier certificates (CBC), as a discretization-free approach, to synthesize safety controllers for stochastic hybrid systems while providing safety guarantees in finite time horizons. In our proposed scheme, we first provide an augmented framework to characterize each stochastic hybrid system containing continuous evolutions and instantaneous jumps with a unified system covering both scenarios. We then introduce an augmented control barrier certificate (ACBC) for augmented systems and propose sufficient conditions to construct an ACBC based on CBC of original hybrid systems. By utilizing the constructed ACBC, we quantify upper bounds on the probability that the stochastic hybrid system reaches certain unsafe regions in a finite time horizon. The proposed approach is verified over a nonlinear case study.
In this paper, we propose a compositional framework for the construction of control barrier certificates for large-scale stochastic switched systems accepting multiple control barrier certificates with some dwell-time conditions. The proposed scheme is based on a notion of so-called augmented pseudo-barrier certificates computed for each switched subsystem, using which one can compositionally synthesize state-feedback controllers for interconnected systems enforcing safety specifications over a finite-time horizon. In particular, we first leverage sufficient max-type small-gain conditions to c…
This paper is concerned with a compositional scheme for the construction of control barrier certificates for interconnected discrete-time stochastic systems. The main objective is to synthesize switching control policies against $ω$-regular properties that can be described by accepting languages of deterministic Streett automata (DSA) along with providing probabilistic guarantees for the satisfaction of such specifications. The proposed framework leverages the interconnection topology and a notion of so-called \emph{control sub-barrier certificates} of subsystems, which are used to composition…
This paper is concerned with a compositional approach for the construction of control barrier certificates for large-scale interconnected stochastic systems while synthesizing hybrid controllers against high-level logic properties. Our proposed methodology involves decomposition of interconnected systems into smaller subsystems and leverages the notion of control sub-barrier certificates of subsystems, enabling one to construct control barrier certificates of interconnected systems by employing some max-type small-gain conditions. The main goal is to synthesize hybrid controllers enforcing com…
In this paper, we propose the safety barrier certificates for uncertain multi-robot systems playing red light, green light game. According to the rule of the game, the robots are allowed to move forward after a doll shouts `green light' and must stop when it shouts `red light'. Following this rule, a two-mode nominal controller is designed where one mode is for moving forward and the other one is for slowing down and being motionless. Then, multiple exponential control barrier functions(ECBFs) are developed to handle safety constraints for limited playground, collision avoidance, and saturatio…
Hyperproperties are system properties that require quantification over multiple execution traces of a system. Hyperproperties can express several specifications of interest for cyber-physical systems--such as opacity, robustness, and noninterference--which cannot be expressed using linear-time properties. This paper presents for the first time a discretization-free approach for the formal verification of discrete-time uncertain dynamical systems against hyperproperties. The proposed approach involves decomposition of complex hyperproperties into several verification conditions by exploiting th…
This paper is motivated by the increasing security concerns of cyber-physical systems. Here, we develop a discretization-free verification scheme targeting an information-flow security property, called approximate initial-state opacity, for the class of discrete-time control systems. We propose notions of so-called augmented control barrier certificates in conjunction with specified regions of interest capturing the initial and secret sets of the system. Sufficient conditions for (the lack of) approximate initial-state opacity of discrete-time control systems are proposed based on the existenc…
The paper presents a methodology for temporal logic verification of continuous-time switched stochastic systems. Our goal is to find the lower bound on the probability that a complex temporal property is satisfied over a finite time horizon. The required temporal properties of the system are expressed using a fragment of linear temporal logic, called safe-LTL with respect to finite traces. Our approach combines automata-based verification and the use of barrier certificates. It relies on decomposing the automaton associated with the negation of specification into a sequence of simpler reachabi…
Converse Barrier Certificates for Finite-time Safety Verification of Continuous-time Perturbed Deterministic Systems
Key Lab. of System Software (Chinese Academy of Sciences), Institute of Software, CAS（中国科学院软件研究所系统软件重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）；School of Mathematics and Physics, University of Science and Technology Beijing（北京科技大学数理学院）
Converse Barrier Certificates for Set-Based Stochastic Reach-Avoid Verification
Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；College of Computing and Data Science, Nanyang Technological University（南洋理工大学计算与数据科学学院）
In this paper, we propose a data-driven approach to formally verify the safety of (potentially) unknown discrete-time continuous-space stochastic systems. The proposed framework is based on a notion of barrier certificates together with data collected from trajectories of unknown systems. We first reformulate the barrier-based safety verification as a robust convex problem (RCP). Solving the acquired RCP is hard in general because not only the state of the system lives in a continuous set, but also and more problematic, the unknown model appears in one of the constraints of RCP. Instead, we le…
In this work we formulate the satisfaction of a (syntactically co-safe) linear temporal logic specification on a physical plant through a recent hybrid dynamical systems formalism. In order to solve this problem, we introduce an extension to such a hybrid system framework of the so-called eventuality property, which matches suitably the condition for the satisfaction of such a temporal logic specification. The eventuality property can be established through barrier certificates, which we derive for the considered hybrid system framework. Using a hybrid barrier certificate, we propose a solutio…
Autonomous Cyber-Physical Systems (CPS) fuse proprioceptive sensors such as GPS and exteroceptive sensors including Light Detection and Ranging (LiDAR) and cameras for state estimation and environmental observation. It has been shown that both types of sensors can be compromised by malicious attacks, leading to unacceptable safety violations. We study the problem of safety-critical control of a LiDAR-based system under sensor faults and attacks. We propose a framework consisting of fault tolerant estimation and fault tolerant control. The former reconstructs a LiDAR scan with state estimations…
Safe Reach Set Computation via Neural Barrier Certificates
University of Oxford（牛津大学）；Newcastle University（纽卡斯尔大学）；Max Planck Institute for Software Systems（马克斯·普朗克软件系统研究所）；Università di Roma “La Sapienza”（罗马第一大学）
Safety in terms of collision avoidance for multi-robot systems is a difficult challenge under uncertainty, non-determinism and lack of complete information. This paper aims to propose a collision avoidance method that accounts for both measurement uncertainty and motion uncertainty. In particular, we propose Probabilistic Safety Barrier Certificates (PrSBC) using Control Barrier Functions to define the space of admissible control actions that are probabilistically safe with formally provable theoretical guarantee. By formulating the chance constrained safety set into deterministic control cons…
This paper focuses on synthesizing control policies for discrete-time stochastic control systems together with a lower bound on the probability that the systems satisfy the complex temporal properties. The desired properties of the system are expressed as linear temporal logic (LTL) specifications over finite traces. In particular, our approach decomposes the given specification into simpler reachability tasks based on its automata representation. We then propose the use of so-called \emph{control barrier certificate} to solve those simpler reachability tasks along with computing the correspon…
Southwest University（西南大学）；University of Surrey（萨里大学）；University of York（约克大学）
We provide a novel approach to synthesize controllers for nonlinear continuous dynamical systems with control against safety properties. The controllers are based on neural networks (NNs). To certify the safety property we utilize barrier functions, which are represented by NNs as well. We train the controller-NN and barrier-NN simultaneously, achieving a verification-in-the-loop synthesis. We provide a prototype tool nncontroller with a number of case studies. The experiment results confirm the feasibility and efficacy of our approach.
In this work, we propose a compositional scheme for the safety controller synthesis of interconnected discrete-time stochastic systems with Markovian switching signals. Our proposed approach is based on a notion of so-called control storage certificates computed for individual subsystems, by leveraging which, one can synthesize state-feedback controllers for interconnected systems to enforce safety specifications over finite time horizons. To do so, we employ a sum-of-squares (SOS) optimization approach to search for multiple storage certificates of each switching subsystem while synthesizing …
Performing swift and agile maneuvers is essential for the safe operation of autonomous mobile robots. Moreover, the presence of time-delay restricts the response time of the system and hinders the safety performance. Thus, this paper proposes a modular and scalable safety-control design that utilizes the Smith predictor and barrier certificates to safely and consistently avoid obstacles with different footprints. The proposed solution includes a two-layer predictor to compensate for the time-delay in the servo-system and angle control loops. The proposed predictor configuration dramatically im…
Massachusetts Institute of Technology（麻省理工学院）；University of California, San Diego（加州大学圣地亚哥分校）
Learning-enabled control systems have demonstrated impressive empirical performance on challenging control problems in robotics, but this performance comes at the cost of reduced transparency and lack of guarantees on the safety or stability of the learned controllers. In recent years, new techniques have emerged to provide these guarantees by learning certificates alongside control policies -- these certificates provide concise, data-driven proofs that guarantee the safety and stability of the learned control system. These methods not only allow the user to verify the safety of a learned cont…
