Automatic Reachability Analysis for Nonlinear Hybrid Models with C2E2

Fan, Chuchu; Qi, Bolun; Mitra, Sayan; Viswanathan, Mahesh; Duggirala, Parasara Sridhar

doi:10.1007/978-3-319-41528-4_29

Cited by 86 publications

(66 citation statements)

References 14 publications

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“…Other methods for this class of systems have used simulations for formal analysis, where individual executions are bloated according to model-specific discrepancy functions [22], as implemented in tools such as C2E2 [20,23]. Another analysis approach for nonlinear systems uses Taylor models, such as those in Flow* [15], which can scale to around ten real variables [16].…”

Section: Related Workmentioning

confidence: 99%

Numerical verification of affine systems with up to a billion dimensions

Bak

Tran

Johnson

2019

Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control

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Affine systems reachability is the basis of many verification methods. With further computation, methods exist to reason about richer models with inputs, nonlinear differential equations, and hybrid dynamics. As such, the scalability of affine systems verification is a prerequisite to scalable analysis for more complex systems. In this paper, we improve the scalability of affine systems verification, in terms of the number of dimensions (variables) in the system.The reachable states of affine systems can be written in terms of the matrix exponential, and safety checking can be performed at specific time steps with linear programming. Unfortunately, for large systems with many state variables, this direct approach requires an intractable amount of memory while using an intractable amount of computation time. We overcome these challenges by combining several methods that leverage common problem structure. Memory is reduced by exploiting initial states that are not full-dimensional and safety properties (outputs) over a few linear projections of the state variables. Computation time is saved by using numerical simulations to compute only projections of the matrix exponential relevant for the verification problem. Since large systems often have sparse dynamics, we use Krylov-subspace simulation approaches based on the Arnoldi or Lanczos iterations. Our method produces accurate counter-examples when properties are violated and, in the extreme case with sufficient problem structure, can analyze a system with one billion real-valued state variables. DISTRIBUTION A. Approved for public release; Distribution unlimited. AFRL PA # 88ABW-

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Section: Related Workmentioning

confidence: 99%

Numerical verification of affine systems with up to a billion dimensions

Bak

Tran

Johnson

2019

Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control

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“…Backward reachability has been extensively used for verifying performance and safety of systems [25], [26]. There are a plethora of tools for computing BRSs for many different classes of system models [27]- [29]. Since the traditional focus of backward reachability has been on providing performance and safety guarantees, computations of BRSs are expensive.…”

Section: Related Workmentioning

confidence: 99%

BaRC: Backward Reachability Curriculum for Robotic Reinforcement Learning

Ivanovic

Harrison

Sharma

et al. 2019

2019 International Conference on Robotics and Automation (ICRA)

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Model-free Reinforcement Learning (RL) offers an attractive approach to learn control policies for highdimensional systems, but its relatively poor sample complexity often necessitates training in simulated environments. Even in simulation, goal-directed tasks whose natural reward function is sparse remain intractable for state-of-the-art model-free algorithms for continuous control. The bottleneck in these tasks is the prohibitive amount of exploration required to obtain a learning signal from the initial state of the system. In this work, we leverage physical priors in the form of an approximate system dynamics model to design a curriculum for a model-free policy optimization algorithm. Our Backward Reachability Curriculum (BaRC) begins policy training from states that require a small number of actions to accomplish the task, and expands the initial state distribution backwards in a dynamically-consistent manner once the policy optimization algorithm demonstrates sufficient performance. BaRC is general, in that it can accelerate training of any model-free RL algorithm on a broad class of goal-directed continuous control MDPs. Its curriculum strategy is physically intuitive, easy-to-tune, and allows incorporating physical priors to accelerate training without hindering the performance, flexibility, and applicability of the model-free RL algorithm. We evaluate our approach on two representative dynamic robotic learning problems and find substantial performance improvement relative to previous curriculum generation techniques and naïve exploration strategies. Aeronautics and Astronautics,

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“…The idea was pioneered in [10] and implemented in Breach [9] with sound generalization guarantees for linear models based on sensitivity analysis. Subsequently the idea has been extended to nonlinear, hybrid, and black-box systems and implemented in tools like C2E2 and DryVR [12,19,17,16].…”

Section: Introductionmentioning

confidence: 99%

Multi-agent Safety Verification Using Symmetry Transformations

Sibai

Mokhlesi

Fan

et al. 2020

Tools and Algorithms for the Construction and Analysis of Systems

Self Cite

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We show that symmetry transformations and caching can enable scalable, and possibly unbounded, verification of multi-agent systems. Symmetry transformations map solutions and to other solutions. We show that this property can be used to transform cached reachsets to compute new reachsets, for hybrid and multi-agent models. We develop a notion of virtual system which define symmetry transformations for a broad class of agent models that visit waypoint sequences. Using this notion of virtual system, we present a prototype tool CacheReach that builds a cache of reachtubes for this system, in a way that is agnostic of the representation of the reachsets and the reachability analysis subroutine used.Our experimental evaluation of CacheReach shows up to 66% savings in safety verification computation time on multi-agent systems with 3-dimensional linear and 4-dimensional nonlinear fixed-wing aircraft models following sequences of waypoints. These savings and our theoretical results illustrate the potential benefits of using symmetry-based caching in the safety verification of multi-agent systems.

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Automatic Reachability Analysis for Nonlinear Hybrid Models with C2E2

Cited by 86 publications

References 14 publications

Numerical verification of affine systems with up to a billion dimensions

Numerical verification of affine systems with up to a billion dimensions

BaRC: Backward Reachability Curriculum for Robotic Reinforcement Learning

Multi-agent Safety Verification Using Symmetry Transformations

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