Search results for "state space"
showing 9 items of 49 documents
Variable Length Memory Chains: Characterization of stationary probability measures
2021
Variable Length Memory Chains (VLMC), which are generalizations of finite order Markov chains, turn out to be an essential tool to modelize random sequences in many domains, as well as an interesting object in contemporary probability theory. The question of the existence of stationary probability measures leads us to introduce a key combinatorial structure for words produced by a VLMC: the Longest Internal Suffix. This notion allows us to state a necessary and sufficient condition for a general VLMC to admit a unique invariant probability measure. This condition turns out to get a much simpler form for a subclass of VLMC: the stable VLMC. This natural subclass, unlike the general case, enj…
Quantitative ergodicity for some switched dynamical systems
2012
International audience; We provide quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space Rd × E where E is a finite set. The continuous component evolves according to a smooth vector field that switches at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Under regularity assumptions on the jump rates and stability conditions for the vector fields we provide explicit exponential upper bounds for the convergence to equilibrium in terms of Wasserstein distances. As an example, we obtain convergence results for a stochastic version of the Morris-Lecar model of neurobiology.
Verification of linear hybrid systems with large discrete state spaces using counterexample-guided abstraction refinement
2017
Abstract We present a counterexample-guided abstraction refinement ( CEGAR) approach for the verification of safety properties of linear hybrid automata with large discrete state spaces, such as naturally arising when incorporating health state monitoring and degradation levels into the controller design. Such models can – in contrast to purely functional controller models – not be analyzed with hybrid verification engines relying on explicit representations of modes, but require fully symbolic representations for both the continuous and discrete part of the state space. The presented abstraction methods directly work on a symbolic representation of arbitrary non-convex combinations of line…
Wind Shear On-Line Identification for Unmanned Aerial Systems
2014
An algorithm to perform the on line identification of the wind shear components suitable for the UAS characteristics has been implemented. The mathematical model of aircraft and wind shear in the augmented state space has been built without any restrictive assumption on the dynamic of wind shear. Due to the severe accelerations on the aircraft induced by the strong velocity variation typical of wind shear, the wind shear effects have been modeled as external forces and moments applied on the aircraft. The identification problem addressed in this work has been solved by using the Filter error method approach. An Extended Kalman Filter has been developed to propagate state. It has been tuned …
Théorie de système et séries temporelles
1994
The aim of this paper is to present a different representation of state space models, (innovation state space representation) which is relatively new and apparently unknown in the economics and econometrics literature and to describe some of its properties. state space representation is a very flexible form for time series and the approach taken in this paper therefore allows a broad class of models it does not impose a priori the decomposition of data series into trend and cycle
Density flow over networks: A mean-field game theoretic approach
2014
A distributed routing control algorithm for dynamic networks has recently been presented in the literature. The networks were modeled using time evolution of density at network edges and the routing control algorithm allowed edge density to converge to a Wardrop equilibrium, which was characterized by an equal traffic density on all used paths. We borrow the idea and rearrange the density model to recast the problem within the framework of mean-field games. The contribution of this paper is three-fold. First, we provide a mean-field game formulation of the problem at hand. Second, we illustrate an extended state space solution approach. Third, we study the stochastic case where the density …
Modelling Without a Modelling Language
2018
Developments in computer hardware and programming languages, in this case C++, have made it feasible to write models of concurrent systems under verification in the programming language, instead of some established modelling language such as Promela. While this does not reduce the usefulness of modelling languages, it offers new possibilities that may be advantageous, for instance, when teaching state space ideas to newcomers or when experimenting with new scientific ideas. In earlier work, we were able to express everything else fairly naturally in C++, except the set of transitions. The present study uses C++ lambda functions to represent naturally transitions that consist of a tail state…
Prediction and interpolation of time series by state space models
2015
Artikkeliväitöskirja. Sisältää yhteenveto-osan ja neljä artikkelia. Article dissertation. Contains an introduction part and four articles. A large amount of data collected today is in the form of a time series. In order to make realistic inferences based on time series forecasts, in addition to point predictions, prediction intervals or other measures of uncertainty should be presented. Multiple sources of uncertainty are often ignored due to the complexities involved in accounting them correctly. In this dissertation, some of these problems are reviewed and some new solutions are presented. A state space approach is also advocated for an e cient and exible framework for time series forecas…
Parental and Infant Gender Factors in Parent-Infant Interaction: State-Space Dynamic Analysis.
2017
This study aimed to investigate the influence of parental gender on their interaction with their infants, considering, as well, the role of the infant’s gender. The State Space Grid (SSG) method, a graphical tool based on the non-linear dynamic system (NDS) approach was used to analyze the interaction, in Free-Play setting, of 52 infants, aged 6 to 10 months, divided into two groups: half of the infants interacted with their fathers and half with their mothers. There were 50% boys in each group. MANOVA results showed no differential parenting of boys and girls. Additionally, mothers and fathers showed no differences in the Diversity of behavioral dyadic states nor in Predictability. However…