Tools for Stability of Switching Linear Systems: Gain Automata and Delay Compensation.

The topic of this paper is the analysis of stability for a class of switched linear systems, modeled by hybrid automata. In each location of the hybrid automaton the dynamics is assumed to be linear and asymptotically stable; the guards on the transitions are hyperplanes in the state space. For each location an estimate is made of the gain via a Lyapunov function for the dynamics in that location, given a pair of ingoing and outgoing transitions. It is shown how to obtain the best possible estimate by optimizing the Lyapunov function. The estimated gains are used in defining a so-called gain automaton that forms the basis of an algorithmic criterion for the stability of the hybrid automaton. The associated gain automaton provides a systematic tool to detect potential sources of instability as well as an indication on to how to stabilize the hybrid systems by requiring appropriate delays for specific transitions

Re-verification of a Lip Synchronization Algorithm using robust reachability

The timed automata formalism is an important model for specifying and analysing real-time systems. Robustness is the correctness of the model in the presence of small drifts on clocks or imprecision in testing guards. A symbolic algorithm for the analysis of the robustness of timed automata has been implemented. In this paper we re-analyse an industrial case lip synchronization protocol using the new robust reachability algorithm.This lip synchronization protocol is an interesting case because timing aspect are crucial for the correctness of the protocol. Several versions of the model are considered, with an ideal video stream, with anchored jitter, and with non-anchored jitter

Stability criteria for planar linear systems with state reset

In this work we perform a stability analysis for a class of switched linear systems, modeled as hybrid automata. We deal with a switched linear planar system, modeled by a hybrid automaton with one discrete state. We assume the guard on the transition is a line in the state space and the reset map is a linear projection onto the x-axis. We define necessary and sufficient conditions for stability of the switched linear system with fixed and arbitrary dynamics in the location. \u

Setting Parameters for Biological Models With ANIMO

ANIMO (Analysis of Networks with Interactive MOdeling) is a software for modeling biological networks, such as e.g. signaling, metabolic or gene networks. An ANIMO model is essentially the sum of a network topology and a number of interaction parameters. The topology describes the interactions between biological entities in form of a graph, while the parameters determine the speed of occurrence of such interactions. When a mismatch is observed between the behavior of an ANIMO model and experimental data, we want to update the model so that it explains the new data. In general, the topology of a model can be expanded with new (known or hypothetical) nodes, and enables it to match experimental data. However, the unrestrained addition of new parts to a model causes two problems: models can become too complex too fast, to the point of being intractable, and too many parts marked as "hypothetical" or "not known" make a model unrealistic. Even if changing the topology is normally the easier task, these problems push us to try a better parameter fit as a first step, and resort to modifying the model topology only as a last resource. In this paper we show the support added in ANIMO to ease the task of expanding the knowledge on biological networks, concentrating in particular on the parameter settings

Stochastic simulation of event structures

Currently the semantics of stochastic process algebras are defined using (an extension) of labelled transition systems. This usually results in a semantics based on the interleaving of causally independent actions. The advantage is that the structure of transition systems closely resembles that of Markov chains, enabling the use of standard solution techniques for analytical and numerical performance assessment of formal specifications. The main drawback is that distributions are restricted to be exponential. In [2] we proposed to use a partial-order semantics for stochastic process algebras. This allows the support of non-exponential distributions in the process algebra in a perspicuous way, but the direct resemblance with Markov chains is lost. This paper proposes to exploit discrete-event simulation techniques for analyzing our partial-order model, called stochastic event structures. The key idea is to obtain from event structures so-called (time-homogeneous) generalized semiMarkov ..

Comparison of Timed Automata with Discrete Event Simulation for Modeling Personalized Treatment Decisions:the Case of Metastatic Castration Resistant Prostate Cancer

Objectives: The aim of this study is to compare the usefulness of two promising alternative modeling techniques, Timed Automata (TA) originating from informatics, and Discrete Event Simulation (DES) known in operations research, for modeling todays complex and personalized treatment decisions over time, involving multiple interactions and decision gates. Methods: The usefulness of both modeling techniques was assessed in a case study on the treatment of metastatic Castration Resistant Prostate Cancer (mCRPC) in which Circulating Tumor Cells (CTC) may be used as a response marker for switching first to second line treatment. Techniques were compared on user-friendliness, input requirements, input possibilities, model checking facilities, and results. Input parameters were similar for both models, consisting of costs, QoL, treatment effectiveness, diagnostic performance, physicians’ behavior and survival. Primary outcome measures were health outcomes, expressed in QALYs, and costs. Results: Modelling was considered easier using TA, as this approach allows independent modeling of the actors and elements comprising the treatment process, such as patients, physicians, tests and treatments, and their mutual interaction and communication. Furthermore, the statistical model checking feature in the TA software was found to be a powerful tool for validation. Input requirements and possibilities were similar for both modelling approaches in this case study. Both modelling approaches yield comparable results. Using TA, CTC reduced first and second line treatment by, on average, 108.9 and 107.6 days, respectively. Using DES, treatment was reduced by 83.6 and 85.0 days. CTC therefore reduced healthcare costs by €28,998 and €21,992 according to TA and DES, respectively. Conclusions: Both Timed Automata and Discrete Event Simulation seem to be suitable for modeling complex and personalized treatment processes like that of mCRPC. Timed Automata is a new and interesting alternative modeling technique, as it allows explicit separation of model components and supports statistical model checking to validate models

Modeling Biological Pathway Dynamics With Timed Automata

Living cells are constantly subjected to a plethora of environmental stimuli that require integration into an appropriate cellular response. This integration takes place through signal transduction events that form tightly interconnected networks. The understanding of these networks requires to capture their dynamics through computational support and models. ANIMO (Analysis of Networks with Interactive MOdelling) is a tool that enables construction and exploration of executable models of biological networks, helping to derive hypotheses and to plan wet-lab experiments. The tool is based on the formalism of Timed Automata, which can be analysed via the UPPAAL model checker. Thanks to Timed Automata, we can provide a formal semantics for the domain-specific language used to represent signalling networks. This enforces precision and uniformity in the definition of signalling pathways, contributing to the integration of isolated signalling events into complex network models. We propose an approach to discretization of reaction kinetics that allows us to efficiently use UPPAAL as the computational engine to explore the dynamic behaviour of the network of interest. A user-friendly interface hides the use of Timed Automata from the user, while keeping the expressive power intact. Abstraction to single-parameter kinetics speeds up construction of models that remain faithful enough to provide meaningful insight. The resulting dynamic behaviour of the network components is displayed graphically, allowing for an intuitive and interactive modelling experience

Deriving a Graph Rewriting System from a Complete Finite Prefix of an Unfolding

The starting point of this paper is McMillan's complete finite prefix of an unfolding that has been obtained from a Petri net or a process algebra expression. The paper addresses the question of how to obtain the (possibly infinite) system behaviour from the complete finite prefix. An algorithm is presented to derive from the prefix a graph rewriting system that can be used to construct the unfolding. It is shown how to generate event sequences from the graph rewriting system which is important for constructing an interactive simulator. Finally it is indicated how the graph rewriting system yields a transition system that can be used for model checking and test derivation