Ishanu Chattopadhyay

Language-measure-theoretic optimal control of probabilistic finite-state systems

Supervisory control theory for discrete event systems, introduced by Ramadge and Wonham, is based on a non-probabilistic formal language framework. However, models for physical processes inherently involve modelling errors and noise-corrupted observations, implying that any practical finite-state approximation would require consideration of event occurrence probabilities. Building on the concept of signed real measure of regular languages, this paper formulates a comprehensive theory for optimal control of finite-state probabilistic processes. It is shown that the resulting discrete-event supervisor is optimal in the sense of elementwise maximizing the renormalized langauge measure vector for the controlled plant behaviour and is efficiently computable. The theoretical results are validated through several examples including the simulation of an engineering problem.

Structural transformations of probabilistic finite state machines

Probabilistic finite state machines have recently emerged as a viable tool for modelling and analysis of complex non-linear dynamical systems. This paper rigorously establishes such models as finite encodings of probability measure spaces defined over symbol strings. The well known Nerode equivalence relation is generalized in the probabilistic setting and pertinent results on existence and uniqueness of minimal representations of probabilistic finite state machines are presented. The binary operations of probabilistic synchronous composition and projective composition, which have applications in symbolic model-based supervisory control and in symbolic pattern recognition problems, are introduced. The results are elucidated with numerical examples and are validated on experimental data for statistical pattern classification in a laboratory environment.

Information fusion for object & situation assessment in sensor networks

A semantic framework for information fusion in sensor networks for object and situation assessment is proposed. The overall vision is to construct machine representations that would enable human-like perceptual understanding of observed scenes via fusion of heterogeneous sensor data. In this regard, a hierarchical framework is proposed that is based on the Data Fusion Information Group (DFIG) model. Unlike a simple set-theoretic information fusion methodology that leads to loss of information, relational dependencies are modeled as cross-machines called relational Probabilistic Finite State Automata using the xD-Markov machine construction. This leads to a tractable approach for modeling composite patterns as structured sets for both object and scene representation. An illustrative example demonstrates the superior capability of the proposed methodology for pattern classification in urban scenarios.

ν☆: a robot path planning algorithm based on renormalised measure of probabilistic regular languages

This article introduces a novel path planning algorithm, called ν ☆, that reduces the problem of robot path planning to optimisation of a probabilistic finite state automaton. The ν ☆-algorithm makes use of renormalised measure ν of regular languages to plan the optimal path for a specified goal. Although the underlying navigation model is probabilistic, the ν ☆-algorithm yields path plans that can be executed in a deterministic setting with automated optimal trade-off between path length and robustness under dynamic uncertainties. The ν ☆-algorithm has been experimentally validated on Segway Robotic Mobility Platforms in a laboratory environment.

Abductive learning of quantized stochastic processes with probabilistic finite automata

We present an unsupervised learning algorithm (GenESeSS) to infer the causal structure of quantized stochastic processes, defined as stochastic dynamical systems evolving over discrete time, and producing quantized observations. Assuming ergodicity and stationarity, GenESeSS infers probabilistic finite state automata models from a sufficiently long observed trace. Our approach is abductive; attempting to infer a simple hypothesis, consistent with observations and modelling framework that essentially fixes the hypothesis class. The probabilistic automata we infer have no initial and terminal states, have no structural restrictions and are shown to be probably approximately correct-learnable. Additionally, we establish rigorous performance guarantees and data requirements, and show that GenESeSS correctly infers long-range dependencies. Modelling and prediction examples on simulated and real data establish relevance to automated inference of causal stochastic structures underlying complex physical phenomena.

Unsupervised inductive learning in symbolic sequences via Recursive Identification of Self-Similar Semantics

This paper presents a new pattern discovery algorithm for constructing probabilistic finite state automata (PFSA) from symbolic sequences. The new algorithm, described as Compression via Recursive Identification of Self-Similar Semantics (CRISSiS), makes use of synchronizing strings for PFSA to localize particular states and then recursively identifies the rest of the states by computing the n-step derived frequencies. We compare our algorithm to other existing algorithms, such as D-Markov and Casual-State Splitting Reconstruction (CSSR) and show both theoretically and experimentally that our algorithm captures a larger class of models.

Probabilistic fault diagnosis in discrete event systems

This paper presents a concept of discrete-event probabilistic fault diagnosis as an extension of the binary decision approach proposed by Sampath et al., where unobservable failure events are included in the representation of the system behavior under both normal and faulty conditions. It is assumed that the probability of each transition is known at the time of decision making. Based on this finite-state automaton model, probabilistic reasoning is applied for on-line diagnosis of dynamical systems. The major advantage of this approach is early detection of multi-component faults, which facilitates robust reconfiguration of the decision and control system.

Inverse Gillespie for inferring stochastic reaction mechanisms from intermittent samples

Gillespie stochastic simulation is used extensively to investigate stochastic phenomena in many fields, ranging from chemistry to biology to ecology. The inverse problem, however, has remained largely unsolved: How to reconstruct the underlying reactions de novo from sparse observations. A key challenge is that often only aggregate concentrations, proportional to the population numbers, are observable intermittently. We discovered that under specific assumptions, the set of relative population updates in phase space forms a convex polytope whose vertices are indicative of the dominant underlying reactions. We demonstrate the validity of this simple principle by reconstructing stochastic models (reaction structure plus propensities) from a variety of simulated and experimental systems, where hundreds and even thousands of reactions may be occurring in between observations. In some cases, the inferred models provide mechanistic insight. This principle can lead to the understanding of a broad range of phenomena, from molecular biology to population ecology.

Automated behaviour recognition in mobile robots using symbolic dynamic filtering

This paper introduces a dynamic data-driven method for signature detection in mobile robots. The core concept of the paper is built upon the principles of symbolic dynamic filtering (SDF) that can be used to extract relevant information in complex dynamical systems. The objective here is to identify the robot behaviour in real time as accurately as possible. The proposed method is validated by experimentation on a networked robotics test bed to detect and identify the type and motion profile of the robots under consideration.

A language measure for partially observed discrete event systems

Recent literature has introduced and validated a signed real measure of regular languages for quantitative analysis and synthesis of discrete-event supervisory (DES) control systems, where all events are assumed to be observable. This paper presents a modification of the language measure for supervisory control under partial observation and shows how to generalize the analysis when some of the events may not be observable at the supervisory level. In the context of DES control synthesis, the language measure of partially observable discrete-event processes is expressed in a closed form which is structurally similar to that of completely observable discrete-event processes. Examples are provided to elucidate the concept of DES control under partial observation.