179 research outputs found
On weighted time optimal control for linear hybrid automata using quantifier elimination
This paper considers the optimal control problem for linear hybrid automata. In particular, it is shown that the problem can be transformed into a constrained optimization problem whose constraints are a set of inequalities with quantifiers. Quantifier Elimination (QE) techniques are employed in order to derive quantifier free inequalities that are linear. The optimal cost is obtained using linear programming. The optimal switching times and optimal continuous control inputs are computed and used in order to derive the optimal hybrid controller. Our results areapplied to an air traffic management example
Reachability in Biochemical Dynamical Systems by Quantitative Discrete Approximation (extended abstract)
In this paper, a novel computational technique for finite discrete
approximation of continuous dynamical systems suitable for a significant class
of biochemical dynamical systems is introduced. The method is parameterized in
order to affect the imposed level of approximation provided that with
increasing parameter value the approximation converges to the original
continuous system. By employing this approximation technique, we present
algorithms solving the reachability problem for biochemical dynamical systems.
The presented method and algorithms are evaluated on several exemplary
biological models and on a real case study.Comment: In Proceedings CompMod 2011, arXiv:1109.104
Graph transformation systems, Petri nets and Semilinear Sets: Checking for the Absence of Forbidden Paths in Graphs
We introduce an analysis method that checks for the absence of (Euler) paths or cycles in the set of graphs reachable from a start graph via graph transformation rules. This technique is based on the approximation of graph transformation systems by Petri nets and on semilinear sets of markings. An important application is deadlock analysis in distributed systems
Reachability computation for hybrid systems with Ariadne
Ariadne is an in-progress open environment to design algorithms for computing with hybrid automata, that relies on a rigorous computable analysis theory to represent
geometric objects, in order to achieve provable approximation bounds along the computations. In this paper we discuss the problem of reachability analysis of hybrid automata to decide safety properties. We describe in details the algorithm used in Ariadne to compute over-approximations of reachable sets. Then we show how it works on a simple example. Finally, we discuss the lower-approximation approach to the reachability problem and how to extend
Ariadne to support it
Parameter Synthesis for Markov Models
Markov chain analysis is a key technique in reliability engineering. A
practical obstacle is that all probabilities in Markov models need to be known.
However, system quantities such as failure rates or packet loss ratios, etc.
are often not---or only partially---known. This motivates considering
parametric models with transitions labeled with functions over parameters.
Whereas traditional Markov chain analysis evaluates a reliability metric for a
single, fixed set of probabilities, analysing parametric Markov models focuses
on synthesising parameter values that establish a given reliability or
performance specification . Examples are: what component failure rates
ensure the probability of a system breakdown to be below 0.00000001?, or which
failure rates maximise reliability? This paper presents various analysis
algorithms for parametric Markov chains and Markov decision processes. We focus
on three problems: (a) do all parameter values within a given region satisfy
?, (b) which regions satisfy and which ones do not?, and (c)
an approximate version of (b) focusing on covering a large fraction of all
possible parameter values. We give a detailed account of the various
algorithms, present a software tool realising these techniques, and report on
an extensive experimental evaluation on benchmarks that span a wide range of
applications.Comment: 38 page
Kronecker representation and decompositional analysis of closed queueing networks with phase-type service distributions and arbitrary buffer sizes
Two approximative fixed-point iterative methods based on decomposition for closed queueing networks with Coxian service distributions and arbitrary buffer sizes are extended to include phase-type service distributions. The irreducible Markov chain associated with each subnetwork in the respective decompositions is represented hierarchically using Kronecker products. The two methods are implemented in a software tool capable of computing the steady-state probability vector of each subnetwork by a multilevel method at each fixed-point iteration and are compared with other methods for accuracy and efficiency. Numerical results indicate that there is a niche filled by the two approximative methods
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