Related papers: Parameter Synthesis for Cardiac Cell Hybrid Models…
Biological systems are often modeled as a system of ordinary differential equations (ODEs) with time-invariant parameters. However, cell signaling events or pharmacological interventions may alter the cellular state and induce multi-mode…
In this paper we present recent results on parametric analysis of biological models. The underlying method is based on the algorithms for computing trajectory sets of hybrid systems with polynomial dynamics. The method is then applied to…
Formal design of embedded and cyber-physical systems relies on mathematical modeling. In this paper, we consider the model class of hybrid automata whose dynamics are defined by affine differential equations. Given a set of time-series…
We consider the parameter synthesis problem of parametric timed automata (PTAs). The problem is, given a PTA and a property, to compute the set of valuations of the parameters under which the resulting timed automaton satisfies the…
We propose an algorithmic approach for synthesizing linear hybrid automata from time-series data. Unlike existing approaches, our approach provides a whole family of models. Each model in the family is guaranteed to capture the input data…
The aim of this work is to address issues where formal specifications cannot be realized on a given dynamical system subjected to a changing environment. Such failures occur whenever the dynamics of the system restrict the robot in such a…
Modeling biological processes is a highly demanding task because not all processes are fully understood. Mathematical models allow us to test hypotheses about possible mechanisms of biological processes. The mathematical mechanisms…
Delays are ubiquitous in modern hybrid systems, which exhibit both continuous and discrete dynamical behaviors. Induced by signal transmission, conversion, the nature of plants, and so on, delays may appear either in the continuous…
We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid…
Piecewise smooth hybrid systems, involving continuous and discrete variables, are suitable models for describing the multiscale regulatory machinery of the biological cells. In hybrid models, the discrete variables can switch on and off…
Scientific analysis often relies on the ability to make accurate predictions of a system's dynamics. Mechanistic models, parameterized by a number of unknown parameters, are often used for this purpose. Accurate estimation of the model…
We present the framework of delta-complete analysis for bounded reachability problems of general hybrid systems. We perform bounded reachability checking through solving delta-decision problems over the reals. The techniques take into…
We present a new method for the automated synthesis of safe and robust Proportional-Integral-Derivative (PID) controllers for stochastic hybrid systems. Despite their widespread use in industry, no automated method currently exists for…
The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
We consider the feedback design for stabilizing a rigid body system by making and breaking multiple contacts with the environment without prespecifying the timing or the number of occurrence of the contacts. We model such a system as a…
Clinical guidance systems have been widely adopted to help medical staffs to avoid preventable medical errors such as delay in diagnosis, treatment or untended deviations from best practice guidelines. However, because patient condition…
This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…
Parameterizing mathematical models of biological systems often requires fitting to stable periodic data. In cardiac electrophysiology this typically requires converging to a stable action potential through long simulations. We explore this…
In this paper, we study the parameter synthesis problem for a class of parametric timed automata. The problem asks to construct the set of valuations of the parameters in the parametric timed automa- ton, referred to as the feasible region,…