Derek Riley

Computational Methods for Verification of Stochastic Hybrid Systems

Stochastic hybrid system (SHS) models can be used to analyze and design complex embedded systems that operate in the presence of uncertainty and variability. Verification of reachability properties for such systems is a critical problem. Developing sound computational methods for verification is challenging because of the interaction between the discrete and the continuous stochastic dynamics. In this paper, we propose a probabilistic method for verification of SHSs based on discrete approximations focusing on reachability and safety problems. We show that reachability and safety can be characterized as a viscosity solution of a system of coupled Hamilton-Jacobi-Bellman equations. We present a numerical algorithm for computing the solution based on discrete approximations that are derived using finite-difference methods. An advantage of the method is that the solution converges to the one for the original system as the discretization becomes finer. We also prove that the algorithm is polynomial in the number of states of the discrete approximation. Finally, we illustrate the approach with two benchmarks: a navigation and a room heater example, which have been proposed for hybrid system verification.

Computational methods for reachability analysis of stochastic hybrid systems

Stochastic hybrid system models can be used to analyze and design complex embedded systems that operate in the presence of uncertainty and variability. Verification of reachability properties for such systems is a critical problem. Developing algorithms for reachability analysis is challenging because of the interaction between the discrete and continuous stochastic dynamics. In this paper, we propose a probabilistic method for reachability analysis based on discrete approximations. The contribution of the paper is twofold. First, we show that reachability can be characterized as a viscosity solution of a system of coupled Hamilton-Jacobi-Bellman equations. Second, we present a numerical method for computing the solution based on discrete approximations and we show that this solution converges to the one for the original system as the discretization becomes finer. Finally, we illustrate the approach with a navigation benchmark that has been proposed for hybrid system verification.

NCSWT: An integrated modeling and simulation tool for networked control systems

Abstract Networked Control Systems (NCS) are becoming increasingly ubiquitous in a growing number of applications, such as groups of unmanned aerial vehicles and industrial control systems. The evaluation of NCS properties such as stability and performance is very important given that these systems are typically deployed in critical settings. This paper presents the Networked Control Systems Wind Tunnel (NCSWT), an integrated modeling and simulation tool for the evaluation of Networked Control Systems (NCS). NCSWT integrates Matlab/Simulink and ns-2 for modeling and simulation of NCS using the High Level Architecture (HLA) standard. The tool is composed of two parts, the design-time models and the run-time components. The design-time models use Model Integrated Computing (MIC) to define HLA-based model constructs such as federates representing the simulators and interactions representing the communication between the simulators. MIC techniques facilitate the modeling and design of complex systems by using abstractions defined in domain-specific modeling languages (DSMLs) to describe the systems. The design-time models represent the control system dynamics and networking system behaviors in order to facilitate the run-time simulation of a NCS. The run-time components represent the main software components and interfaces for the actual realization of a NCS simulation using the HLA framework. Our implementation of the NCSWT based on HLA guarantees accurate time synchronization and data communication. Two case studies are presented to demonstrate the capabilities of the tool as well as evaluate the impact of network effects on NCS.

Modelling and analysis of the sugar cataract development process using stochastic hybrid systems

Modelling and analysis of biochemical systems such as sugar cataract development (SCD) are critical because they can provide new insights into systems, which cannot be easily tested with experiments; however, they are challenging problems due to the highly coupled chemical reactions that are involved. The authors present a stochastic hybrid system (SHS) framework for modelling biochemical systems and demonstrate the approach for the SCD process. A novel feature of the framework is that it allows modelling the effect of drug treatment on the system dynamics. The authors validate the three sugar cataract models by comparing trajectories computed by two simulation algorithms. Further, the authors present a probabilistic verification method for computing the probability of sugar cataract formation for different chemical concentrations using safety and reachability analysis methods for SHSs. The verification method employs dynamic programming based on a discretisation of the state space and therefore suffers from the curse of dimensionality. To analyse the SCD process, a parallel dynamic programming implementation that can handle large, realistic systems was developed. Although scalability is a limiting factor, this work demonstrates that the proposed method is feasible for realistic biochemical systems.

NCSWT: an integrated modeling and simulation tool for networked control systems

This paper presents the Networked Control Systems Windtunnel (NCSWT), an integrated modeling and simulation tool for the evaluation of networked control systems (NCS). NCSWT integrates Matlab/Simulink and ns-2 using the High Level Architecture (HLA). Our implementation of the NCSWT based on HLA guarantees accurate time synchronization and data communication in heterogenous simulations. NCSWT uses the Model Integrated Computing (MIC) techniques to define HLA-based model constructs such as federates representing the simulators and interactions between the simulators. NCSWT also uses MIC techniques to define models representing the control system and network dynamics for the rapid synthesis of simulations.

Modeling and Simulation of Biochemical Processes Using Stochastic Hybrid Systems: The Sugar Cataract Development Process

As biomedical research advances there is an increasing need to model and simulate more complicated systems to better understand them. Since biochemical processes are inherently stochastic and often contain both continuous and discrete behavior, stochastic hybrid systems are an ideal modeling paradigm for capturing their dynamics. In this paper we present a framework for modeling biochemical systems and demonstrate the approach for the sugar cataract development process including two methods of modeling drug treatment. Further, we present a simulation method that uses second-order Taylor approximations for the continuous dynamics and an improved method for detecting boundary hits. We use the sugar cataract development process to demonstrate the results of the method.

Safety analysis of sugar cataract development using stochastic hybrid systems

Modeling and analysis of biochemical systems are important tasks because they can unlock insights into the complicated dynamics of systems which are difficult or expensive to test experimentally. A variety of techniques have been used to model biochemical systems, but the effectiveness of the analysis techniques is often limited by tradeoffs imposed by the modeling paradigms. Stochastic differential equations have been used to model biochemical reactions [5,2]; however, analysis of these models has mainly been limited to simulation. Hybrid systems have also been used to model biochemical systems [4]; however, verification methods based on deterministic hybrid systems fail to capture the probabilistic nature of some biochemical processes and therefore may not be able to correctly analyze certain systems. Stochastic Hybrid Systems (SHS) have been used to capture the stochastic nature of biochemical systems but have previously only been used for simulations [10] or analysis of systems with simplified continuous dynamics [6].

Reachability analysis of a biodiesel production system using stochastic hybrid systems

Modeling and analysis of chemical reactions are critical problems because they can provide new insights into the complex interactions between systems of reactions and chemicals. One such set of chemical reactions defines the creation of biodiesel from soybean oil and methanol. Modeling and analyzing the biodiesel creation process is a challenging problem due to the highly-coupled chemical reactions that are involved. In this paper we model a biodiesel production system as a stochastic hybrid system, and we present a probabilistic verification method for reachability analysis. Our analysis can potentially provide useful insights into the complicated dynamics of the chemicals and assist in focusing experiments and tuning the production system for efficiency. The verification method employs dynamic programming based on a discretization of the state space and therefore suffers from the curse of dimensionality. To verify the biodiesel system model we have developed a parallel dynamic programming implementation that can handle large systems. Although scalability is a limiting factor, this work demonstrates that the technique is feasible for realistic biochemical systems.

Predictive analytics on Electronic Health Records (EHRs) using Hadoop and Hive

Healthcare industry is providing massive amounts of patient data. The need for parallel processing is apparent for mining these data sets to provide personalized medicine or advice to patients. An EHR data management system is essential to provide insights and predict outcomes from past patient data. In this paper, we present an EHR data management system to process massive amounts of healthcare data. The system is built on Hive, which is scalable and dynamic compared to traditional data warehouses. Patient data can be uploaded to Hive from a variety of sources like flat files, web pages, real-time applications and databases. Unlike traditional data warehouses, used for transaction processing and analytics, Hive is used for analytics only. The data can be easily sent to Reports application to generate graphs and charts from the Hive data warehouse. The graphical charts are useful for doctors and researchers to understand and propose medications based on evidence from a large number of past patient records. The predictive analysis is helpful to treat patients using specific medications, based on a number of factors such as lifestyle, family history, smoking habits, and health conditions such as blood pressure and diabetes.

Verification of Biochemical Processes Using Stochastic Hybrid Systems

Modeling and analysis of biochemical systems are critical problems because they can provide new insights into systems which can not be easily tested with real experiments. One such biochemical process is the formation of sugar cataracts in the lens of an eye. Analyzing the sugar cataract development process is a challenging problem due to the highly-coupled chemical reactions that are involved. In this paper we model sugar cataract development as a stochastic hybrid system. Based on this model, we present a probabilistic verification method for computing the probability of sugar cataract formation for different chemical concentrations. Our analysis can potentially provide useful insights into the complicated dynamics of the process and assist in focusing experiments on specific regions of concentrations. The verification method employs dynamic programming based on a discretization of the state space and therefore suffers from the curse of dimensionality. To verify the sugar cataract development process we have developed a parallel dynamic programming implementation that can handle large systems. Although scalability is a limiting factor, this work demonstrates that the technique is feasible for realistic biochemical systems.