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Register a new userBarrier Certificates Revisited
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Added by
Dai Liyun
Publication date
2013
fields
Informatics Engineering
and research's language is
English
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A barrier certificate can separate the state space of a con- sidered hybrid system (HS) into safe and unsafe parts ac- cording to the safety property to be verified. Therefore this notion has been widely used in the verification of HSs. A stronger condition on barrier certificates means that less expressive barrier certificates can be synthesized. On the other hand, synthesizing more expressive barrier certificates often means high complexity. In [9], Kong et al consid- ered how to relax the condition of barrier certificates while still keeping their convexity so that one can synthesize more expressive barrier certificates efficiently using semi-definite programming (SDP). In this paper, we first discuss how to relax the condition of barrier certificates in a general way, while still keeping their convexity. Particularly, one can then utilize different weaker conditions flexibly to synthesize dif- ferent kinds of barrier certificates with more expressiveness efficiently using SDP. These barriers give more opportuni- ties to verify the considered system. We also show how to combine two functions together to form a combined barrier certificate in order to prove a safety property under consid- eration, whereas neither of them can be used as a barrier certificate separately, even according to any relaxed condi- tion. Another contribution of this paper is that we discuss how to discover certificates from the general relaxed condi- tion by SDP. In particular, we focus on how to avoid the unsoundness because of numeric error caused by SDP with symbolic checking
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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.
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 unbounded-time safety of differential dynamical systems. The proposed condition is by far the least conservative one on barrier certificates, and can be shown as the weakest possible one to attain inductive invariance. We show that discharging the invariant barrier-certificate condition -- thereby synthesizing invariant barrier certificates -- can be encoded as solving an optimization problem subject to bilinear matrix inequalities (BMIs). We further propose a synthesis algorithm based on difference-of-convex programming, which approaches a local optimum of the BMI problem via solving a series of convex optimization problems. This algorithm is incorporated in a branch-and-bound framework that searches for the global optimum in a divide-and-conquer fashion. We present a weak completeness result of our method, in the sense that a barrier certificate is guaranteed to be found (under some mild assumptions) whenever there exists an inductive invariant (in the form of a given template) that suffices to certify safety of the system. Experimental results on benchmark examples demonstrate the effectiveness and efficiency of our approach.
We study the multi-agent safe control problem where agents should avoid collisions to static obstacles and collisions with each other while reaching their goals. Our core idea is to learn the multi-agent control policy jointly with learning the control barrier functions as safety certificates. We propose a novel joint-learning framework that can be implemented in a decentralized fashion, with generalization guarantees for certain function classes. Such a decentralized framework can adapt to an arbitrarily large number of agents. Building upon this framework, we further improve the scalability by incorporating neural network architectures that are invariant to the quantity and permutation of neighboring agents. In addition, we propose a new spontaneous policy refinement method to further enforce the certificate condition during testing. We provide extensive experiments to demonstrate that our method significantly outperforms other leading multi-agent control approaches in terms of maintaining safety and completing original tasks. Our approach also shows exceptional generalization capability in that the control policy can be trained with 8 agents in one scenario, while being used on other scenarios with up to 1024 agents in complex multi-agent environments and dynamics.
Reactive and safe agent modelings are important for nowadays traffic simulator designs and safe planning applications. In this work, we proposed a reactive agent model which can ensure safety without comprising the original purposes, by learning only high-level decisions from expert data and a low-level decentralized controller guided by the jointly learned decentralized barrier certificates. Empirical results show that our learned road user simulation models can achieve a significant improvement in safety comparing to state-of-the-art imitation learning and pure control-based methods, while being similar to human agents by having smaller errors to the expert data. Moreover, our learned reactive agents are shown to generalize better to unseen traffic conditions, and react better to other road users and therefore can help understand challenging planning problems pragmatically.
Recent advances in Deep Machine Learning have shown promise in solving complex perception and control loops via methods such as reinforcement and imitation learning. However, guaranteeing safety for such learned deep policies has been a challenge due to issues such as partial observability and difficulties in characterizing the behavior of the neural networks. While a lot of emphasis in safe learning has been placed during training, it is non-trivial to guarantee safety at deployment or test time. This paper extends how under mild assumptions, Safety Barrier Certificates can be used to guarantee safety with deep control policies despite uncertainty arising due to perception and other latent variables. Specifically for scenarios where the dynamics are smooth and uncertainty has a finite support, the proposed framework wraps around an existing deep control policy and generates safe actions by dynamically evaluating and modifying the policy from the embedded network. Our framework utilizes control barrier functions to create spaces of control actions that are safe under uncertainty, and when the original actions are found to be in violation of the safety constraint, uses quadratic programming to minimally modify the original actions to ensure they lie in the safe set. Representations of the environment are built through Euclidean signed distance fields that are then used to infer the safety of actions and to guarantee forward invariance. We implement this method in simulation in a drone-racing environment and show that our method results in safer actions compared to a baseline that only relies on imitation learning to generate control actions.
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