Estimations of solutions convergence of hybrid systems with delay

Estimations are given for solutions of hybrid systems with delays, by using Lyapunov-Krasovsky functionals

Decision algorithm for the stability of planar switching linear systems

This paper presents a decision algorithm for the analysis of the stability of a class of planar switched linear systems, modeled by hybrid automata. The dynamics in each location of the hybrid automaton is assumed to be linear and asymptotically stable; the guards on the transitions are hyper planes in the state space. We show that for every pair of an ingoing and an outgoing transition related to a location, the exact gain in the norm of the vector induced by the dynamics in that location can be computed. These exact gains are used in defining a gain automaton which forms the basis of an algorithmic criterion to determine if a planar hybrid automaton is stable or not

Stability Analysis for Hybrid Automata Using Conservative Gains

This paper presents a stability analysis approach for a class of hybrid\ud automata. It is assumed that the dynamics in each location of the hybrid automaton is linear and asymptotically stable, and that the guards on the transitions are hyperplanes in the state space. For each pair of ingoing and outgoing transitions in a location a conservative estimate is made of the gain via a Lyapunov function for the dynamics in that location. It is shown how the choice of the Lyapunov function can be optimized to obtain the best possible estimate. The calculated conservative 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

A narrative review on spinal deformities in people with cerebral palsy: Measurement, norm values, incidence, risk factors and treatment

Spinal deformities are common in people with cerebral palsy (CP), and there is a concern of an increase during the adult ageing period. There is especially a worry about the increase of scoliosis, thoracic hyperkyphosis, lumbar hyperlordosis, spondylolysis and spondylolisthesis incidence, though supporting literature is lacking. Therefore, the aim of this narrative review is to provide a scientific overview of how spinal curvatures should be measured, what the norm values are and the incidence in people with CP, as well as a description of the risk factors and the treatment regimens for these spinal abnormalities. This review can be used as a guideline relevant for a range of clinicians, including orthopaedic and neurosurgeons, radiologists, physiotherapists, and biokineticists, as well as academics

PRM113 - Timed Automata Modeling of The Personalized Treatment Decisions In Metastatic Castration Resistant Prostate Cancer

Objectives\ud The Timed Automata modeling paradigm has emerged from Computer Science as a mature tool for the functional analysis and performance evaluation of timed distributed systems. This study is a first exploration of the suitability of Timed Automata for health economic modeling, using a case study on personalized treatment for metastatic Castration Resistant Prostate Cancer (mCRPC).\ud \ud Methods\ud The treatment process has been modeled by creating several independent timed automata, where an automaton represents a patient, a physician, a test, or a treatment/testing guideline schedule. These automata interact via message passing and are fully parameterized with quantitative information. Messages can be passed, asynchronously, from one automaton to one or more other automata, at any point in time, thereby triggering events and decisions in the treatment process. In the automata time is continuous, and both QALYs and costs can be incorporated using (assignable) local clocks. Uncertainty can be modeled using probabilities and timing intervals that can be uniformly or exponentially distributed. Software for building timed automata is freely available for academic use and includes procedures for statistical model checking (SMC) to validate the (internal) behavior and results of the model.\ud \ud Results\ud In several days a Timed Automata model has been produced that is compositional, easy to understand and easy to update. The behavior and results of the model have been assessed using the SMC tool. Actual results for the mCRPC case study obtained from the Timed Automata model are compared with results of a Discrete Event Simulation model in a separate study.\ud \ud Conclusions\ud The Timed Automata paradigm can be successfully applied to evaluate the potential benefits of a personalized treatment process of mCRPC. The compositional nature of the resulting model provides a good separation of all relevant components. This leads to models that are easy to formulate, validate, understand, maintain and update

From POOSL to UPPAAL : transformation and quantitative analysis

POOSL (Parallel Object-Oriented Specification Language) is a powerful general purpose system-level modeling language. In research on design space exploration of motion control systems, POOSL has been used to construct models for performance analysis. The considered motion control algorithms are characterized by periodic execution. They are executed by multiple processors, which are interconnected by Rapid Input/Output (RapidIO) packet switches. Packet latencies as worst-case latencies and average-case latencies are essential performance criteria for motion control systems. However, POOSL analysis merely allows for estimation results for these latency metrics since it is primarily based on simulation. Because motion control systems are time-critical and safety-critical, worst-case latencies of packets are strict timing constraints. Therefore exact worst-case latencies are to be determined. Motivated by this requirement we propose to use model checking techniques. In this paper we illustrate how a POOSL model of a (simplified) motion control system can be transformed into an UPPAAL model and we verify its functional behavior and worst-case latencies. Moreover, we show that analysis of average-case latencies can also be accomplished with assistance of the model checking tool UPPAAL

UPPAAL in practice : quantitative verification of a RapidIO network.

Packet switched networks are widely used for interconnecting distributed computing platforms. RapidIO (Rapid Input/Output) is an industry standard for packet switched networks to interconnect multiple processor boards. Key performance metrics for these platforms include average-case and worst-case packet transfer latencies. We focus on verifying such quantitative properties for a RapidIO based multi-processor platform that executes a motion control application. A performance model is available in the Parallel Object-Oriented Specification Language (POOSL) that allows for simulation based estimation results. It is however required to determine the exact worst-case latency as the application is time-critical. A model checking approach has been proposed in our previous work which transforms the POOSL model into an UPPAAL model. However, such an approach only works for a fairly small system. We extend the transformation approach with various heuristics to reduce the underlying state space, thereby providing an effective approximation approach that scales to industrial problems of a reasonable complexity