14,056 research outputs found
Extending Hybrid CSP with Probability and Stochasticity
Probabilistic and stochastic behavior are omnipresent in computer controlled
systems, in particular, so-called safety-critical hybrid systems, because of
fundamental properties of nature, uncertain environments, or simplifications to
overcome complexity. Tightly intertwining discrete, continuous and stochastic
dynamics complicates modelling, analysis and verification of stochastic hybrid
systems (SHSs). In the literature, this issue has been extensively
investigated, but unfortunately it still remains challenging as no promising
general solutions are available yet. In this paper, we give our effort by
proposing a general compositional approach for modelling and verification of
SHSs. First, we extend Hybrid CSP (HCSP), a very expressive and process
algebra-like formal modeling language for hybrid systems, by introducing
probability and stochasticity to model SHSs, which is called stochastic HCSP
(SHCSP). To this end, ordinary differential equations (ODEs) are generalized by
stochastic differential equations (SDEs) and non-deterministic choice is
replaced by probabilistic choice. Then, we extend Hybrid Hoare Logic (HHL) to
specify and reason about SHCSP processes. We demonstrate our approach by an
example from real-world.Comment: The conference version of this paper is accepted by SETTA 201
Bounded Verification with On-the-Fly Discrepancy Computation
Simulation-based verification algorithms can provide formal safety guarantees
for nonlinear and hybrid systems. The previous algorithms rely on user provided
model annotations called discrepancy function, which are crucial for computing
reachtubes from simulations. In this paper, we eliminate this requirement by
presenting an algorithm for computing piece-wise exponential discrepancy
functions. The algorithm relies on computing local convergence or divergence
rates of trajectories along a simulation using a coarse over-approximation of
the reach set and bounding the maximal eigenvalue of the Jacobian over this
over-approximation. The resulting discrepancy function preserves the soundness
and the relative completeness of the verification algorithm. We also provide a
coordinate transformation method to improve the local estimates for the
convergence or divergence rates in practical examples. We extend the method to
get the input-to-state discrepancy of nonlinear dynamical systems which can be
used for compositional analysis. Our experiments show that the approach is
effective in terms of running time for several benchmark problems, scales
reasonably to larger dimensional systems, and compares favorably with respect
to available tools for nonlinear models.Comment: 24 page
Model-based compositional verification approaches and tools development for cyber-physical systems
The model-based design for embedded real-time systems utilizes the veriable reusable components and proper architectures, to deal with the verification scalability problem caused by state-explosion. In this thesis, we address verification approaches for both low-level individual component correctness and high-level system correctness, which are equally important under this scheme. Three prototype tools are developed, implementing our approaches and algorithms accordingly.
For the component-level design-time verification, we developed a symbolic verifier, LhaVrf, for the reachability verification of concurrent linear hybrid systems (LHA). It is unique in translating a hybrid automaton into a transition system that preserves the discrete transition structure, possesses no continuous dynamics, and preserves reachability of discrete states. Afterward, model-checking is interleaved in the counterexample fragment based specification relaxation framework. We next present a simulation-based bounded-horizon reachability analysis approach for the reachability verification of systems modeled by hybrid automata (HA) on a run-time basis. This framework applies a dynamic, on-the-fly, repartition-based error propagation control method with the mild requirement of Lipschitz continuity on the continuous dynamics. The novel features allow state-triggered discrete jumps and provide eventually constant over-approximation error bound for incremental stable dynamics. The above approaches are implemented in our prototype verifier called HS3V. Once the component properties are established, the next thing is to establish the system-level properties through compositional verication. We present our work on the role and integration of quantier elimination (QE) for property composition and verication. In our approach, we derive in a single step, the strongest system property from the given component properties for both time-independent and time-dependent scenarios. The system initial condition can also be composed, which, alongside the strongest system property, are used to verify a postulated system property through induction. The above approaches are implemented in our prototype tool called ReLIC
Analytic real-time analysis and timed automata: a hybrid methodology for the performance analysis of embedded real-time systems
This paper presents a compositional and hybrid approach for the performance analysis of distributed real-time systems. The developed methodology abstracts system components by either flow-oriented and purely analytic descriptions or by state-based models in the form of timed automata. The interaction among the heterogeneous components is modeled by streams of discrete events. In total this yields a hybrid framework for the compositional analysis of embedded systems. It supplements contemporary techniques for the following reasons: (a) state space explosion as intrinsic to formal verification is limited to the level of isolated components; (b) computed performance metrics such as buffer sizes, delays and utilization rates are not overly pessimistic, because coarse-grained analytic models are used only for components that conform to the stateless model of computation. For demonstrating the usefulness of the presented ideas, a corresponding tool-chain has been implemented. It is used to investigate the performance of a two-staged computing system, where one stage exhibits state-dependent behavior that is only coarsely coverable by a purely analytic and stateless component abstraction. Finally, experiments are performed to ascertain the scalability and the accuracy of the proposed approac
Algebraic verification of hybrid systems in Isabelle/HOL
The thesis describes an open modular semantic framework for the verification of hybrid systems in a general-purpose proof assistant. We follow this approach to create the first algebraic based verification components for hybrid systems in Isabelle/HOL.
The framework benefits from various design choices. Firstly, an algebra for programs such as Kleene algebras with tests or modal Kleene algebras captures the verification condition generation by providing rules for each programming construct. Intermediate relational or state transformer semantics instantiated to a concrete model of the program store allow the framework to handle assignments and ordinary differential equations (ODEs). The verification rules for ODEs require user-provided solutions, differential invariants or analytical descriptions of the continuous dynamics of the system.
The construction is a shallow embedding which makes the approach quickly extensible and modular. Taking advantage of these features, we derive differential Hoare logic (dH), a minimalistic logic for the verification of hybrid systems, and the differential refinement calculus (dR) for their stepwise construction. Yet the approach is not limited to these formalisms. We also present a hybrid weakest liberal precondition calculus based on predicate transformers which subsumes powerful deductive verification approaches like differential dynamic logic.
The framework is also compositional: we combine it with lenses to vary the model of the program store. We also support it with a formalisation of affine and linear systems of ordinary differential equations in Isabelle/HOL. This integration simplifies various certifications that the proof assistant requires such as guarantees of existence and uniqueness of the corresponding solutions.
Verification examples illustrate the approach at work. Formalisations of our solutions to problems of the international friendly competition ARCH2020, where our components participated, further evidence their effectiveness. Finally, a larger case study certifying an invariant for a PID controller of the roll angle in a quadcopter’s flight complements these verifications
Compositional Verification for Autonomous Systems with Deep Learning Components
As autonomy becomes prevalent in many applications, ranging from
recommendation systems to fully autonomous vehicles, there is an increased need
to provide safety guarantees for such systems. The problem is difficult, as
these are large, complex systems which operate in uncertain environments,
requiring data-driven machine-learning components. However, learning techniques
such as Deep Neural Networks, widely used today, are inherently unpredictable
and lack the theoretical foundations to provide strong assurance guarantees. We
present a compositional approach for the scalable, formal verification of
autonomous systems that contain Deep Neural Network components. The approach
uses assume-guarantee reasoning whereby {\em contracts}, encoding the
input-output behavior of individual components, allow the designer to model and
incorporate the behavior of the learning-enabled components working
side-by-side with the other components. We illustrate the approach on an
example taken from the autonomous vehicles domain
HYPE: Hybrid modelling by composition of flows
Abstract
Hybrid systems are manifest in both the natural and the engineered world, and their complex nature, mixing discrete control and continuous evolution, make it difficult to predict their behaviour. In recent years several process algebras for modelling hybrid systems have appeared in the literature, aimed at addressing this problem. These all assume that continuous variables in the system are modelled monolithically, often with differential equations embedded explicitly in the syntax of the process algebra expression. In HYPE an alternative approach is taken which offers finer-grained modelling with each flow or influence affecting a variable modelled separately. The overall behaviour then emerges as the composition of flows. In this paper we give a detailed account of the HYPE process algebra, its semantics, and its use for verification of systems. We establish both syntactic conditions (well-definedness) and operational restrictions (well-behavedness) to ensure reasonable behaviour in HYPE models. Furthermore we consider how the equivalence relation defined for HYPE relates to other relations previously proposed in the literature, demonstrating that our fine-grained approach leads to a more discriminating notion of equivalence. We present the HYPE model of a standard hybrid system example, both establishing that our approach can reproduce the previously obtained results and demonstrating how our compositional approach supports variations of the problem in a straightforward and flexible way
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