David Thorsley

Diagnosability of stochastic discrete-event systems

We investigate diagnosability of stochastic discrete-event systems. We define the notions of A- and AA-diagnosability for stochastic automata; these notions are weaker than the corresponding notion of diagnosability for logical automata introduced by Sampath et al. Through the construction of a stochastic diagnoser, we determine offline conditions necessary and sufficient to guarantee A-diagnosability and sufficient to guarantee AA-diagnosability. We also show how the stochastic diagnoser can be used for on-line diagnosis of failure events. We illustrate the results through two examples from HVAC systems.

Active Acquisition of Information for Diagnosis and Supervisory Control of Discrete Event Systems

This paper considers the problems of fault diagnosis and supervisory control in discrete event systems through the context of a new observation paradigm. For events that are considered observable, a cost is incurred each time a sensor is activated in an attempt to make an event observation. In such a situation the best strategy is to perform an “active acquisition” of information, i.e. to choose which sensors need to be activated based on the information state generated from the previous readings of the system. Depending on the sample path executed by the system, different sensors may be turned on or off at different stages of the process. We consider the active acquisition of information problem for both logical and stochastic discrete event systems. We consider three classes of increasing complexity: firstly, for acyclic systems where events are synchronized to clock ticks; secondly, for acyclic untimed systems; and lastly, for general cyclic automata. For each of these cases we define a notion of information state for the problem, determine conditions for the existence of an optimal policy, and construct a dynamic program to find an optimal policy where one exists. For large systems, a limited lookahead algorithm for computational savings is proposed.

Diagnosability of stochastic discrete-event systems under unreliable observations

We investigate diagnosability of stochastic discrete-event systems where the observation of certain events is unreliable, that is, there are non-zero probabilities of the misdetection and misclassification of events based on faulty sensor readings. Such sensor unreliability is unavoidable in applications such as nuclear energy generation. We propose the notions of uA- and uAA-diagnosability for stochastic automata and demonstrate their relationship with the concepts of A- and AA-diagnosabilty defined previously. We extend the concept of the stochastic diagnoser to the unreliable observation paradigm and find conditions for uA- and uAA-diagnosability.

Intrusion Detection in Controlled Discrete Event Systems

The constituent controllers in a supervisory control system may sometimes fail as a result of an intruder interfering with the feedback performance of the system. The intrusion may allow the system to execute traces that the supervisor wishes to prevent from occurring. We derive conditions under which a supervisor can detect the presence of an intruder in time to prevent the execution of an illegal trace. In situations where it is not possible to block all illegal strings, we use a language measure method to assess the damage caused by a particular set of controllers failing. We also use the language measure technique to determine the optimal behavior of the controlled system in the presence of an intrusion

Model reduction of stochastic processes using Wasserstein pseudometrics

We consider the problem of finding reduced models of stochastic processes. We use Wasserstein pseudometrics to quantify the difference between processes. The method proposed in this paper is applicable to any continuous-time stochastic process with output, and pseudometrics between processes are defined only in terms of the available outputs. We demonstrate how to approximate a wide class of behavioral pseudometrics and how to optimize parameter values to minimize Wasserstein pseudometrics between processes. In particular, we introduce an algorithm that allows for the approximation of Wasserstein pseudometrics from sampled data, even in the absence of models for the processes. We illustrate the approach with an example from systems biology.

Hidden Markov Models for non-well-mixed reaction networks

The behavior of systems of stochastically interacting particles, be they molecules comprising a chemical reaction network or multi-robot systems in a stochastic environment, can be described using the Chemical Master Equation (CME). In this paper we extend the applicability of the CME to the case when the underlying system of particles is not well-mixed, by constructing an extended state space. The proposed approach fits into the general framework of approximating stochastic processes by Hidden Markov Models (HMMs). We consider HMMs where the hidden states are equivalence classes of states of some underlying process. The sets of equivalence classes we consider are refinements of macrostates used in the CME. We construct a series of HMMs that use the CME to describe their hidden states. We demonstrate the approach by building a series of increasingly accurate models for a system of robots that interact in a non-well-mixed manner.

Estimation and Discrimination of Stochastic Biochemical Circuits from Time-Lapse Microscopy Data

The ability of systems and synthetic biologists to observe the dynamics of cellular behavior is hampered by the limitations of the sensors, such as fluorescent proteins, available for use in time-lapse microscopy. In this paper, we propose a generalized solution to the problem of estimating the state of a stochastic chemical reaction network from limited sensor information generated by microscopy. We mathematically derive an observer structure for cells growing under time-lapse microscopy and incorporates the effects of cell division in order to estimate the dynamically-changing state of each cell in the colony. Furthermore, the observer can be used to discrimate between models by treating model indices as states whose values do not change with time. We derive necessary and sufficient conditions that specify when stochastic chemical reaction network models, interpreted as continuous-time Markov chains, can be distinguished from each other under both continual and periodic observation. We validate the performance of the observer on the Thattai-van Oudenaarden model of transcription and translation. The observer structure is most effective when the system model is well-parameterized, suggesting potential applications in synthetic biology where standardized biological parts are available. However, further research is necessary to develop computationally tractable approximations to the exact generalized solution presented here.

Sequential window diagnoser for discrete-event systems under unreliable observations

This paper addresses the issue of counting the occurrence of special events in the framework of partially-observed discrete-event dynamical systems (DEDS). Developed diagnosers referred to as sequential window diagnosers (SWDs) utilize the stochastic diagnoser probability transition matrices developed in [9] along with a resetting mechanism that allows on-line monitoring of special event occurrences. To illustrate their performance, the SWDs are applied to detect and count the occurrence of special events in a particular DEDS. Results show that SWDs are able to accurately track the number of times special events occur.

Diagnosability of stochastic chemical kinetic systems: a discrete event systems approach

We consider the problem of detecting events of interest in a stochastic chemical kinetic system from the perspective of discrete-event systems theory. We define a class of discrete-event systems, timed stochastic automata, that is well-suited for modeling stochastic chemical kinetics and define tA-tAA-diagnosability, two appropriate notions of diagnosability for this class of system. We develop the construction of a timed stochastic diagnoser that is used to provide online updates of the probability that an event of interest has occurred and a means for offline testing of diagnosability conditions. The results of the paper are illustrated using a model of stochastic gene expression.

Diagnosability of stochastic automata

A methodology for diagnosability of finite-state stochastic automata is established in this paper. Two notions of diagnosability for stochastic automata are defined, and a stochastic analogue of the logical diagnoser is constructed. The stochastic diagnoser is used to (i) specify off-line conditions sufficient to guarantee these notions of diagnosability; and (ii) determine how to perform on-line diagnosis of failure events.