Equivalence of the stability of discrete-time Markov jump linear systems

This paper investigates the stability of discrete-time Markov jump linear system of second-order, this type of system is similar to the family of discrete-time Markov jump linear system it is known in classical literature as MJLS. We present some consistent stability definitions for the system, where these types of stability are equivalent as long as the state space Markov chain is finite. In addition, a computational test is presented to analyze the stability of the system. The result is a generalization of classical theory, this implies a contribution to the theory

Modeling and Stability Analysis of Nonlinear Sampled-Data Systems with Embedded Recovery Algorithms

Computer control systems for safety critical systems are designed to be fault tolerant and reliable, however, soft errors triggered by harsh environments can affect the performance of these control systems. The soft errors of interest which occur randomly, are nondestructive and introduce a failure that lasts a random duration. To minimize the effect of these errors, safety critical systems with error recovery mechanisms are being investigated. The main goals of this dissertation are to develop modeling and analysis tools for sampled-data control systems that are implemented with such error recovery mechanisms. First, the mathematical model and the well-posedness of the stochastic model of the sampled-data system are presented. Then this mathematical model and the recovery logic are modeled as a dynamically colored Petri net (DCPN). For stability analysis, these systems are then converted into piecewise deterministic Markov processes (PDP). Using properties of a PDP and its relationship to discrete-time Markov chains, a stability theory is developed. In particular, mean square equivalence between the sampled-data and its associated discrete-time system is proved. Also conditions are given for stability in distribution to the delta Dirac measure and mean square stability for a linear sampled-data system with recovery logic

Performance Analysis of Recoverable Flight Control Systems Subject to Neutron-Induced Upsets Using Hybrid Dynamical Models

It has been observed that atmospheric neutrons can produce single-event upsets in digital flight control hardware. Potentially, they can reduce system performance and introduce a safety hazard. One experimental system-level approach investigated to help mitigate the effects of these upsets is NASA Langley\u27s Recoverable Computer System. It employs rollback error recovery using dual-lock-step processors together with new fault tolerant architectures and communication subsystems. In this dissertation, a class of stochastic hybrid dynamical models, which consists of a jump-linear system and a stochastic finite-state automaton, is used to describe the performance of a Boeing 737 aircraft system in closed-loop with a Recoverable Computer System. The jump-linear system models the switched dynamics of the closed-loop system due to the presence of controller recoveries. Each dynamical model in the jump-linear system was obtained separately using system identification techniques and high fidelity flight simulation software. The stochastic finite-state automaton approximates the recovery logic of the Recoverable Computer System. The upsets process is modeled by either an independent, identically distributed process or a first-order Markov chain. Mean-square stability and output tracking performance of the recoverable flight control system are analyzed theoretically via a model-equivalent Markov jump-linear system of the stochastic hybrid model. The model was validated using data from a controlled experiment at NASA Langley, where simulated neutron-induced upsets were injected into the system at a desired rate. The effects on the output tracking performance of a simulated aircraft were then directly observed and quantified. The model was then used to analyze a neutron-based experiment on the Recoverable Computer System at the Los Alamos National Laboratory. This model predicts that the experimental flight control system, when functioning as designed, will provide robust control performance in the presence of neutron-induced single-event upsets at normal atmospheric levels

Establishing probability of failure of a system due to electromagnetic interference

Scope and Method of Study:A wire placed inside the metallic box will serve as the equipment under test and the distributions of current and fields will be calculated via measurements. From the distribution, the probability of the observable exceeding a certain threshold can be determined. From the nature of the EME generated, the probability of threat due to EMI can be derived under some assumptions. Combining both the probabilities, the net probability of failure of the system could be determined. Reverberation chambers will be useful in measurements in this study as they simulate operating conditions of the EUT inside a cavity and as the EUT is exposed in all directions to the electromagnetic field, the uncertainty is also reduced. The probability models can provide insight into what type of testing is required to assure worst case testing with reasonable accuracy.Findings and Conclusions:The final outcome of this work is to establish the probability of failure due to current coupled onto a cable or a cable bundle located close to the wall of a cavity due to external or internal coupling of EM. The electromagnetic environment of the cavity was determined to estimate the probability of threat depending on the location of the cable inside the cavity. Given that the probability of threat exists, then the probability that the value of the current exceeding a certain threshold was determined. The environment in which the EUT operates and the influence of the environment on the observable that is being targeted was also determined which aids in the calculation of threshold probability. Finally, the net probability of failure of a system was determined from the individual probabilities. The major focus of this work was on the development of the methodology that is sufficiently general to obtain the distribution of any observable. The procedure developed could be used in different scenarios and from a class of distributions developed for each scenario, the probability of threat and probability of failure of a system due to EMI can be calculated

Fault Injection and Monitoring Capability for a Fault-Tolerant Distributed Computation System

The Configurable Fault-Injection and Monitoring System (CFIMS) is intended for the experimental characterization of effects caused by a variety of adverse conditions on a distributed computation system running flight control applications. A product of research collaboration between NASA Langley Research Center and Old Dominion University, the CFIMS is the main research tool for generating actual fault response data with which to develop and validate analytical performance models and design methodologies for the mitigation of fault effects in distributed flight control systems. Rather than a fixed design solution, the CFIMS is a flexible system that enables the systematic exploration of the problem space and can be adapted to meet the evolving needs of the research. The CFIMS has the capabilities of system-under-test (SUT) functional stimulus generation, fault injection and state monitoring, all of which are supported by a configuration capability for setting up the system as desired for a particular experiment. This report summarizes the work accomplished so far in the development of the CFIMS concept and documents the first design realization