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Vector Barrier Certificates and Comparison Systems [chapter]

Andrew Sogokon, Khalil Ghorbal, Yong Kiam Tan, André Platzer
2018 Lecture Notes in Computer Science  
of vector barrier certificates in safety verification and invariant synthesis.  ...  The paper presents an accessible development of the approach, demonstrates that most previous notions of barrier certificate are special cases of comparison systems, and discusses the potential applications  ...  for their detailed comments and scrutiny.  ... 
doi:10.1007/978-3-319-95582-7_25 fatcat:hrgch7sazvfmdcn2fhjrcbygna

Safety verification of reactive controllers for UAV flight in cluttered environments using barrier certificates

Andrew J. Barry, Anirudha Majumdar, Russ Tedrake
2012 2012 IEEE International Conference on Robotics and Automation  
Using recent advances in sums-ofsquares programming that allow for efficient computation of barrier functions, we search for global certificates of safety for the closed-loop system in a given environment  ...  We expect that these formal verification techniques will allow for the comparison, and ultimately optimization, of reactive controllers for robustness to varying initial conditions and environments.  ...  By constructing a Lyapunovlike function, which they called a "barrier certificate" which was positive inside every obstacle and negative in the initial conditions, and verifying that the vector field could  ... 
doi:10.1109/icra.2012.6225351 dblp:conf/icra/BarryMT12 fatcat:uecirh22bfan3dvyydfylo5idi

Synthesizing Invariant Barrier Certificates via Difference-of-Convex Programming

Qiuye Wang, Mingshuai Chen, Bai Xue, Naijun Zhan, Joost-Pieter Katoen
2021 Lecture Notes in Computer Science  
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  ...  We present a novel condition on barrier certificates, termed the invariant barrier-certificate condition, that witnesses unbounded-time safety of differential dynamical systems.  ...  general barrier certificates [8] and vector barrier certificates [51] .  ... 
doi:10.18154/rwth-2021-06837 fatcat:vrstv3fmebamlfrj6smcgtonhm

Active Sampling-based Binary Verification of Dynamical Systems [article]

John F. Quindlen, Ufuk Topcu, Girish Chowdhary, Jonathan P. How
2018 arXiv   pre-print
However, the nonlinearity of the resulting closed-loop system complicates verification that the system does in fact satisfy those requirements at all possible operating conditions.  ...  Nonlinear, adaptive, or otherwise complex control techniques are increasingly relied upon to ensure the safety of systems operating in uncertain environments.  ...  Approach Analytical barrier certificate techniques are a common solution for verification of nonlinear systems.  ... 
arXiv:1706.04268v2 fatcat:bpee2b7f4revnpi7t6bw3fbe5q

Reachable Set Over-Approximation for Nonlinear Systems Using Piecewise Barrier Tubes [chapter]

Hui Kong, Ezio Bartocci, Thomas A. Henzinger
2018 Lecture Notes in Computer Science  
Experiments on some benchmark systems show that our approach is effective.  ...  a set of barrier functions (called barrier tube or BT for short) which work together to form a tube surrounding the flowpipe.  ...  Each set of the AUSs is used as an unsafe set U i for the system and then we compute a barrier certificate B i for U i according to Theorem 2.  ... 
doi:10.1007/978-3-319-96145-3_24 fatcat:fflqmz4vhfc67coqswcp4qlysq

Learning Safe Neural Network Controllers with Barrier Certificates [article]

Hengjun Zhao, Xia Zeng, Taolue Chen, Zhiming Liu, Jim Woodcock
2020 arXiv   pre-print
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.  ...  B(x) = 0, then the system Γ is safe, and such B is a barrier certificate.  ... 
arXiv:2009.09826v1 fatcat:chuykk5xn5hw7omlrwxo4ivrsi

A Novel Approach for Solving the BMI Problem in Barrier Certificates Generation [chapter]

Xin Chen, Chao Peng, Wang Lin, Zhengfeng Yang, Yifang Zhang, Xuandong Li
2020 Lecture Notes in Computer Science  
Barrier certificates generation is widely used in verifying safety properties of hybrid systems because of the relatively low computational complexity it costs.  ...  Under sum of squares (SOS) relaxation, the problem of barrier certificate generation is equivalent to that of solving a bilinear matrix inequality (BMI) with a particular type.  ...  [34] employed the comparison principle associated with the convex verification conditions, to generate vector barrier certificates in safety verification.  ... 
doi:10.1007/978-3-030-53288-8_29 fatcat:h5wnfdnkazfobfs32ybek5phlu

Unbounded-Time Safety Verification of Stochastic Differential Dynamics [chapter]

Shenghua Feng, Mingshuai Chen, Bai Xue, Sriram Sankaranarayanan, Naijun Zhan
2020 Lecture Notes in Computer Science  
This is achieved by discovering an exponential barrier certificate that proves exponentially converging bounds on the probability of safety violations over time.  ...  They are widely used in numerous applications such as engineered systems (e.g., modeling how pedestrians move in an intersection), computational finance (e.g., modeling stock option prices), and ecological  ...  Particularly, 0 and 1 denote respectively the vector of zeros and ones of appropriate dimension, and the comparison between vectors, e.g., x ≤ 0, is component-wise.  ... 
doi:10.1007/978-3-030-53291-8_18 fatcat:shz67g5jpfbq7jf4zhiqwwl5em

Permissive Barrier Certificates for Safe Stabilization Using Sum-of-squares [article]

Li Wang, Dongkun Han, Magnus Egerstedt
2018 arXiv   pre-print
Motivated by the need to simultaneously guarantee safety and stability of safety-critical dynamical systems, we construct permissive barrier certificates in this paper that explicitly maximize the region  ...  Iterative search algorithms are developed using sum-of-squares to compute the most permissive, that is, the maximum volume, barrier certificates.  ...  Fig. 1 : 1 Comparison of two types of barrier certificates.  ... 
arXiv:1802.08917v1 fatcat:3j6jwslt3zfkjamun4s3wbaqcu

Safe certificate-based maneuvers for teams of quadrotors using differential flatness

Li Wang, Aaron D. Ames, Magnus Egerstedt
2017 2017 IEEE International Conference on Robotics and Automation (ICRA)  
Safety Barrier Certificates that ensure collision-free maneuvers for teams of differential flatness-based quadrotors are presented in this paper.  ...  Synthesized with control barrier functions, the certificates are used to modify the nominal trajectory in a minimally invasive way to avoid collisions.  ...  SAFETY BARRIER CERTIFICATES FOR TEAMS OF QUADROTORS Two of the main tools, i.e., differential flatness property of quadrotor and ECBF for a single quadrotor, for constructing Safety Barrier Certificates  ... 
doi:10.1109/icra.2017.7989375 dblp:conf/icra/WangAE17 fatcat:xc6c4arjujghpkob4ruiwh5oz4

Simulation Based Computation of Certificates for Safety of Hybrid Dynamical Systems [article]

Stefan Ratschan
2018 arXiv   pre-print
In this paper, we present an algorithm for synthesizing certificates---so-called barrier certificates---for safety of hybrid dynamical systems.  ...  Unlike the usual approach of using constraint solvers to compute the certificate from the system dynamics, we synthesize the certificate from system simulations.  ...  The research published in this paper was supported by GAČR grant GA15-14484S and by the long-term strategic development financing of the Institute of Computer Science (RVO:67985807).  ... 
arXiv:1707.00879v6 fatcat:eaew7zbmdjakrhyx6qsxbogxuq

Unbounded-Time Safety Verification of Stochastic Differential Dynamics [article]

Shenghua Feng, Mingshuai Chen, Bai Xue, Sriram Sankaranarayanan, Naijun Zhan
2020 arXiv   pre-print
This is achieved by discovering an exponential barrier certificate that proves exponentially converging bounds on the probability of safety violations over time.  ...  They are widely used in numerous applications such as engineered systems (e.g., modeling how pedestrians move in an intersection), computational finance (e.g., modeling stock option prices), and ecological  ...  Particularly, 0 and 1 denote respectively the vector of zeros and ones of appropriate dimension, and the comparison between vectors, e.g., x ≤ 0, is component-wise.  ... 
arXiv:2006.01858v1 fatcat:rnht75insbdtvm52rvmoztmvqe

Region-of-convergence estimation for learning-based adaptive controllers

John F. Quindlen, Ufuk Topcu, Girish Chowdhary, Jonathan P. How
2016 2016 American Control Conference (ACC)  
These levels sets thus provide barrier certificates for safety and conservatively estimate the complete regionof-convergence. Lastly, the procedure is demonstrated on an adaptive control system.  ...  These level sets can be combined with the a priori known Lyapunov function for such systems to provide barrier certificates, verifying the safety of the system to maximum allowable error limits.  ...  Computation of Barrier Certificates The barrier certificate verifies the safety of the system as long as the system is initialized within the initial set R init .  ... 
doi:10.1109/acc.2016.7525292 dblp:conf/amcc/QuindlenTCH16 fatcat:wfculqi4zrhrdp7dbcxe7jll44

Temporal Logic Verification of Stochastic Systems Using Barrier Certificates [article]

Pushpak Jagtap and Sadegh Soudjani and Majid Zamani
2018 arXiv   pre-print
The proposed approach relies on decomposing the negation of the specification into a union of sequential reachabilities and then using barrier certificates to compute upper bounds for these reachability  ...  We propose to use barrier certificates for computations of such lower bounds, which is computationally much more efficient than the existing discretization-based approaches.  ...  It is based on computation of barrier certificates and uses sum-of-squares optimization to find such bounds.  ... 
arXiv:1807.00064v1 fatcat:glohwzaiyjgujpt6x5rbwpqy3u

A sublinear algorithm for barrier-certificate-based data-driven model validation of dynamical systems

Shuo Han, Ufuk Topcu, George J. Pappas
2015 2015 54th IEEE Conference on Decision and Control (CDC)  
The paper considers the problem of scaling the method of barrier certificates for data-driven validation of dynamical system models using a large number of collected trajectories.  ...  After modifications, the multiplicative weights method is able to yield an exact solution to the convex feasibility problem and hence a valid barrier certificate.  ...  Strictly speaking, the technique of barrier certificates is used to invalidate the system model; if a barrier certificate can be constructed, then the class of system models is invalidated by knowledge  ... 
doi:10.1109/cdc.2015.7402508 dblp:conf/cdc/HanTP15 fatcat:pkec6qfopjdl5dubt3kqgvqrii
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