316 research outputs found
ARCH-COMP19 Category Report: Continuous and hybrid systems with nonlinear dynamics
We present the results of a friendly competition for formal verification of continuous and hybrid systems with nonlinear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2019. In this year, 6 tools Ariadne, CORA, DynIbex, Flow*, Isabelle/HOL, and JuliaReach (in alphabetic order) participated. They are applied to solve reachability analysis problems on four benchmark problems, one of them with hybrid dynamics. We do not rank the tools based on the results, but show the current status and discover the potential advantages of different tools
Enclosing the behavior of a hybrid automaton up to and beyond a Zeno point
Even simple hybrid automata like the classic bouncing ball can exhibit Zeno behavior. The existence of this type of behavior has so far forced a large class of simulators to either ignore some events or risk looping indefinitely. This in turn forces modelers to either insert ad-hoc restrictions to circumvent Zeno behavior or to abandon hybrid automata. To address this problem, we take a fresh look at event detection and localization. A key insight that emerges from this investigation is that an enclosure for a given time interval can be valid independent of the occurrence of a given event. Such an event can then even occur an unbounded number of times. This insight makes it possible to handle some types of Zeno behavior. If the post-Zeno state is defined explicitly in the given model of the hybrid automaton, the computed enclosure covers the corresponding trajectory that starts from the Zeno point through a restarted evolution
LNCS
Template polyhedra generalize intervals and octagons to polyhedra whose facets are orthogonal to a given set of arbitrary directions. They have been employed in the abstract interpretation of programs and, with particular success, in the reachability analysis of hybrid automata. While previously, the choice of directions has been left to the user or a heuristic, we present a method for the automatic discovery of directions that generalize and eliminate spurious counterexamples. We show that for the class of convex hybrid automata, i.e., hybrid automata with (possibly nonlinear) convex constraints on derivatives, such directions always exist and can be found using convex optimization. We embed our method inside a CEGAR loop, thus enabling the time-unbounded reachability analysis of an important and richer class of hybrid automata than was previously possible. We evaluate our method on several benchmarks, demonstrating also its superior efficiency for the special case of linear hybrid automata
Hamilton-Jacobi Reachability Analysis for Hybrid Systems with Controlled and Forced Transitions
Hybrid dynamical systems with non-linear dynamics are one of the most general
modeling tools for representing robotic systems, especially contact-rich
systems. However, providing guarantees regarding the safety or performance of
such hybrid systems can still prove to be a challenging problem because it
requires simultaneous reasoning about continuous state evolution and discrete
mode switching. In this work, we address this problem by extending classical
Hamilton-Jacobi (HJ) reachability analysis, a formal verification method for
continuous non-linear dynamics in the presence of bounded inputs and
disturbances, to hybrid dynamical systems. Our framework can compute reachable
sets for hybrid systems consisting of multiple discrete modes, each with its
own set of non-linear continuous dynamics, discrete transitions that can be
directly commanded or forced by a discrete control input, while still
accounting for control bounds and adversarial disturbances in the state
evolution. Along with the reachable set, the proposed framework also provides
an optimal continuous and discrete controller to ensure system safety. We
demonstrate our framework in simulation on an aircraft collision avoidance
problem, as well as on a real-world testbed to solve the optimal mode planning
problem for a quadruped with multiple gaits
Provably Safe Reinforcement Learning via Action Projection using Reachability Analysis and Polynomial Zonotopes
While reinforcement learning produces very promising results for many
applications, its main disadvantage is the lack of safety guarantees, which
prevents its use in safety-critical systems. In this work, we address this
issue by a safety shield for nonlinear continuous systems that solve
reach-avoid tasks. Our safety shield prevents applying potentially unsafe
actions from a reinforcement learning agent by projecting the proposed action
to the closest safe action. This approach is called action projection and is
implemented via mixed-integer optimization. The safety constraints for action
projection are obtained by applying parameterized reachability analysis using
polynomial zonotopes, which enables to accurately capture the nonlinear effects
of the actions on the system. In contrast to other state-of-the-art approaches
for action projection, our safety shield can efficiently handle input
constraints and dynamic obstacles, eases incorporation of the spatial robot
dimensions into the safety constraints, guarantees robust safety despite
process noise and measurement errors, and is well suited for high-dimensional
systems, as we demonstrate on several challenging benchmark systems
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