Guaranteed Verification of Dynamic Systems

Diese Arbeit beschreibt einen neuen Spezifikations- und Verifikationsansatz für dynamische Systeme. Der neue Ansatz ermöglicht dabei Ergebnisse, die per Definition frei von Fehlern 2. Art sind. Dies bedeutet, dass das Ergebnis der Verifikation keine versteckten Fehler enthalten kann. Somit können zuverlässige Ergebnisse für die Analyse von sicherheitskritischen Systemen generiert werden. Dazu wird ein neues Verständnis von mengenbasierter Konsistenz dynamischer Systeme mit einer gegebenen Spezifikation eingeführt. Dieses basiert auf der Verwendung von Kaucher Intervall Arithmetik zur Einschließung von Messdaten. Konsistenz wird anhand der vereinigten Lösungsmenge der Kaucher Arithmetik definiert. Dies führt zu mathematisch garantierten Ergebnissen. Die resultierende Methode kann das spezifizierte Verhalten eines dynamischen System auch im Falle von Rauschen und Sensorungenauigkeiten anhand von Messdaten verifizieren. Die mathematische Beweisbarkeit der Konsistenz wird für eine große Klasse von Systemen gezeigt. Diese beinhalten zeitinvariante, intervallartige und hybride Systeme, wobei letztere auch zur Beschreibung von Nichtlinearitäten verwendet werden können. Darüber hinaus werden zahlreiche Erweiterungen dargestellt. Diese führen bis hin zu einem neuartigen iterativen Identifikations- und Segmentierungsverfahren für hybride Systeme. Dieses ermöglicht die Verfikation hybrider Systeme auch ohne Wissen über Schaltzeitpunkte. Die entwickelten Verfahren können darüber hinaus zur Diagnose von dynamischen Systemen verwendet werden, falls eine ausreichend schnelle Berechnung der Ergebnisse möglich ist. Die Verfahren werden erfolgreich auf eine beispielhafte Variation verschiedener Tanksysteme angewendet. Die neuen Theorien, Methoden und Algortihmen dieser Arbeit bilden die Grundlage für eine zuverlässige Analyse von hochautomatisierten sicherheitskritischen Systemen

Guaranteed Verification of Dynamic Systems

This work introduces a new specification and verification approach for dynamic systems. The introduced approach is able to provide type II error free results by definition, i.e. there are no hidden faults in the verification result. The approach is based on Kaucher interval arithmetic to enclose the measurement in a bounded error sense. The developed methods are proven mathematically to provide a reliable verification for a wide class of safety critical systems

A robust fault detection method using a zonotopic Kaucher set-membership approach

This paper presents a robust fault detection method using a zonotopic Kaucher set-membership method. The fault detection approach is based on checking the consistency between the model and the data. Consistency is given if there is an intersection between the feasible parameter set and the nominal parameter set. To allow efficient computation the feasible set is approximated by a zonotope. Due to the usage of Kaucher interval arithmetic the results are mathematically guaranteed. The proposed approach is assessed using an illustrative application based on a well-known four-tank case study. The study shows that it is possible to detect even small errors in a noisy settingPeer ReviewedPostprint (published version

Guaranteed Verification of Dynamic Systems

This work introduces a new specification and verification approach for dynamic systems. The introduced approach is able to provide type II error free results by definition, i.e. there are no hidden faults in the verification result. The approach is based on Kaucher interval arithmetic to enclose the measurement in a bounded error sense. The developed methods are proven mathematically to provide a reliable verification for a wide class of safety critical systems

Inner approximated reachability analysis

International audienceComputing a tight inner approximation of the range of a function over some set is notoriously di cult, way beyond obtaining outer approximations. We propose here a new method to compute a tight inner approximation of the set of reachable states of non-linear dynamical systems on a bounded time interval. This approach involves a ne forms and Kaucher arithmetic, plus a number of extra ingredients from set-based methods. An implementation of the method is discussed, and illustrated on representative numerical schemes, discrete-time and continuous-time dynamical systems

High performance with high accuracy laboratory

ln order to obtain high performance with high accuracy in the so lution of scientific computational problems, a computational tool has been developed, called High Performance with High Accuracy Labora tory. ln this paper we describe initially the high performance and then the high accuracy and the interval mathematics. After that , the tool is described, including two environments in which it has been developed, that is, the Cray Supercomputer vector environment and the paral lel environment based on Transputers. The description summarizes the modules, the basic interval library, the high accuracy arithmetic kernel, the interval applied modules, especially the selint.p library. Finally, there are some comments about the performanc

Set-Membership Computation of Admissible Controls for Trajectory Tracking

International audienceIn a context of predictive control strategy, this paper addresses the computation of admissible control set for a trajectory tracking over a prediction horizon. The proposed method combines numerical methods based on set-membership computation and control methods based on a flatness concept. It makes possible i) to provide a guaranteed computation of admissible controls, ii) to deal with uncertain reference trajectory, iii) to reduce the time complexity of the algorithm compared to the existing approach. Simulations illustrate the efficiency of the developed methods in two different cases. For Single Input-Single Output (SISO) systems, generalized affine forms are computed otherwise a Branch & Prune algorithm with an inner inclusion test is used for Multi Inputs-Multi Outputs (MIMO) systems. The computational time is reduced significantly compared to the one required by the existing approach

Backward Reachability Analysis of Perturbed Continuous-Time Linear Systems Using Set Propagation

Backward reachability analysis computes the set of states that reach a target set under the competing influence of control input and disturbances. Depending on their interplay, the backward reachable set either represents all states that can be steered into the target set or all states that cannot avoid entering it -- the corresponding solutions can be used for controller synthesis and safety verification, respectively. A popular technique for backward reachable set computation solves Hamilton-Jacobi-Isaacs equations, which scales exponentially with the state dimension due to gridding the state space. In this work, we instead use set propagation techniques to design backward reachability algorithms for linear time-invariant systems. Crucially, the proposed algorithms scale only polynomially with the state dimension. Our numerical examples demonstrate the tightness of the obtained backward reachable sets and show an overwhelming improvement of our proposed algorithms over state-of-the-art methods regarding scalability, as systems with well over a hundred states can now be analyzed.Comment: 16 page

Computer Aided Verification

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications