Object Oriented Design of Software Tool for Finite Abstractions of Max-Plus-Linear Systems using Unified Modeling Language

Max-Plus-Linear (MPL) systems are a class of discrete-event systems with a continuous state space characterizing the timing of the underlying sequential discrete events. There is a formal approach to analyze these systems based on finite abstractions. The abstraction algorithms have been in MATLAB using list data structure and in JAVA using tree data structure. The MATLAB implementation requires long computational time, whereas the JAVA one requires larger memory allocation. In this work, we discuss an object oriented design in C++ using tree data structure without recursive functions in the hope of improving the results obtained by the two previous implementations

Design And Implementation Of Software For Finite Abstractions Of Max-Plus-Linear Systems Using Tree Without Recursive Functions

Max-Plus-Linear (MPL) systems are a class of discrete-event systems with a continuous state space characterizing the timing of the underlying sequential discrete events. In the literature, there is an approach to analyze these systems based on finite abstractions. This algorithms have been implemented in MATLAB using list/matrix/vector data structure. Disadvantages of this implementation, operation makes the transition requires a long computation time. Then improvement against previous implementation in JAVA using tree data structure. This implementation successfully accelerate computation time but requires a larger memory allocation because its functions are recursive. This thesis discuss implementation in C++ using tree data structure without recursive functions in the hope of improving the results obtained by the two previous implementations

Safety Verification of Uncertain Max-Plus-Linear Systems

In this work, we discussed the verification of autonomous uncertain Max-Plus-Linear (uncertain MPL) systems with respect to safety property by using the reachability analysis approach. More precisely, given an uncertain MPL system, a nonempty set of initial conditions, a time horizon and an unsafe set, we want to determine whether the state can reach the unsafe set within the given time horizon. If the unsafe set is reachable, then the system is not safe. Otherwise, the system is safe. Our approach uses the piecewise affine representation of MPL systems to compute the reachable sets exactly

Formal Analysis and Verification of Max-Plus Linear Systems

Max-Plus Linear (MPL) systems are an algebraic formalism with practical applications in transportation networks, manufacturing and biological systems. In this paper, we investigate the problem of automatically analyzing the properties of MPL, taking into account both structural properties such as transient and cyclicity, and the open problem of user-defined temporal properties. We propose Time-Difference LTL (TDLTL), a logic that encompasses the delays between the discrete time events governed by an MPL system, and characterize the problem of model checking TDLTL over MPL. We first consider a framework based on the verification of infinite-state transition systems, and propose an approach based on an encoding into model checking. Then, we leverage the specific features of MPL systems to devise a highly optimized, combinational approach based on Satisfiability Modulo Theory (SMT). We experimentally evaluate the features of the proposed approaches on a large set of benchmarks. The results show that the proposed approach substantially outperforms the state of the art competitors in expressiveness and effectiveness, and demonstrate the superiority of the combinational approach over the reduction to model checking.Comment: 28 pages (including appendixes

Computational Techniques for Reachability Analysis of Max-Plus-Linear Systems ⋆

Abstract This work discusses a computational approach to reachability analysis of Max-Plus-Linear (MPL) systems, a class of discreteevent systems widely used in synchronization and scheduling applications. Given a set of initial states, we characterize and compute its "reach tube," namely the collection of set of reachable states (regarded step-wise as "reach sets"). By an alternative characterization of the MPL dynamics, we show that the exact computation of the reach sets can be performed quickly and compactly by manipulations of difference-bound matrices, and further derive worst-case bounds on the complexity of these operations. The approach is also extended to backward reachability analysis. The concepts and results are elucidated by a running example, and we further illustrate the performance of the approach by a numerical benchmark: the technique comfortably handles twenty-dimensional MPL systems (i.e., with twenty continuous state variables), and as such it outperforms the state-of-the-art alternative approaches in the literature

Finite Abstractions of Max-Plus-Linear Systems: Theory and Algorithms

Max-Plus-Linear (MPL) systems are a class of discrete-event systems with a continuous state space characterizing the timing of the underlying sequential discrete events. These systems are predisposed to describe the timing synchronization between interleaved processes. MPL systems are employed in the analysis and scheduling of infrastructure networks, such as communication and railway systems, production and manufacturing lines, or biological systems. As a natural extension, Stochastic Max-Plus-Linear (SMPL) systems are MPL systems where the delays between successive events are characterized by random quantities. In practical applications SMPL systems are more realistic than simple MPL ones: for instance in a model for a railway network, train running times depend on driver behavior, on weather conditions, and on passenger numbers at stations. Verification is used to establish whether the system under consideration possesses certain properties expressed as formulae. As an example, reachability analysis is a fundamental problem in the area of formal methods, systems theory, and performance and dependability analysis. It is concerned with assessing whether a certain state of a system is attainable from given initial states of the system. Verification techniques and tools for finite-state systems have been widely investigated and developed in the past decades. However, if the system has a large number of states or even infinitely many states, in general we cannot apply such techniques directly. In this case we need to employ abstraction techniques to formally relate a concrete model to a finite abstraction of it, which is then amenable to be automatically verified by the relevant results in the literature. In this PhD thesis we develop novel abstraction techniques for MPL systems, and use them in an application to communication networks. Additionally we discuss reachability of MPL systems and abstraction techniques for SMPL systems. The abstraction and reachability algorithms for MPL systems developed in this thesis have been implemented as a MATLAB software tool, "Verification via biSimulations of MPL models'' (VeriSiMPL, as in "very simple''), which is freely available for download at http://www.sourceforge.net/projects/verisimpl/.Delft Center for Systems and ControlMechanical, Maritime and Materials Engineerin