Supervisory Control of Fuzzy Discrete Event Systems: A Formal Approach

Fuzzy {\it discrete event systems} (DESs) were proposed recently by Lin and Ying [19], which may better cope with the real-world problems with fuzziness, impreciseness, and subjectivity such as those in biomedicine. As a continuation of [19], in this paper we further develop fuzzy DESs by dealing with supervisory control of fuzzy DESs. More specifically, (i) we reformulate the parallel composition of crisp DESs, and then define the parallel composition of fuzzy DESs that is equivalent to that in [19]; {\it max-product} and {\it max-min} automata for modeling fuzzy DESs are considered; (ii) we deal with a number of fundamental problems regarding supervisory control of fuzzy DESs, particularly demonstrate controllability theorem and nonblocking controllability theorem of fuzzy DESs, and thus present the conditions for the existence of supervisors in fuzzy DESs; (iii) we analyze the complexity for presenting a uniform criterion to test the fuzzy controllability condition of fuzzy DESs modeled by max-product automata; in particular, we present in detail a general computing method for checking whether or not the fuzzy controllability condition holds, if max-min automata are used to model fuzzy DESs, and by means of this method we can search for all possible fuzzy states reachable from initial fuzzy state in max-min automata; also, we introduce the fuzzy $n$-controllability condition for some practical problems; (iv) a number of examples serving to illustrate the applications of the derived results and methods are described; some basic properties related to supervisory control of fuzzy DESs are investigated. To conclude, some related issues are raised for further consideration

Detectability Of Fuzzy Discrete Event Systems

Dynamic systems that can be modeled in terms of discrete states and a synchronous events are known as discrete event systems (DES). A DES is defined in terms of states, events, transition dynamics, and initial state. Knowing the system’s state is crucial in many applications for certain actions (events) to be taken. A DES system is considered a fuzzy discrete event system (FDES) if its states and events are vague in nature; for such systems, the system can be in more than one state at the same time with different degrees of possibility (membership). In this research we introduce a fuzzy discrete event system with constraints (FDESwC) and investigate its detectabilities. This research aims to address the gap in previous studies and extend existing definitions of detectability of DES to include the detectability in systems with substantial vagueness such as FDES. These definitions are first reformulated to introduce N-detectability for DES, which are further extended to define four main types of detectabilities for FDES: strong N-detectability, (weak) N-detectability, strong periodic N-detectability, and (weak) periodic N-detectability. We first partition the FDES into trajectories of a length dictated by the depth of the event’s string (length of the event sequence); each trajectory consists of a number of nodes, which are further investigated for detectability by examining them against the newly introduced certainty criterion. Matrix computation algorithms and fuzzy logic operations are adopted to calculate the state estimates based on the current state and the occurring events. Vehicle dynamics control example is used to demonstrate the practical aspect of developed theorems in real-world applications

Discrete event approach to network fault management

Failure diagnosis in large and complex systems such as a communication network is a critical task. An important aspect of network management is fault management, i.e.,determining, locating, isolation, and correcting faults in the network. In the realm of discrete event systems Sampath et al proposed a failure diagnosis approach, and Jiang et al proposed an efficient algorithm for testing diagnosability. In this work, we adopt the framework of the communicating finite state machine (CFSM) of Miller et al for modeling networks and to investigate fault detection, fault identification and fault location using Sampath et al and Jiang et al methods. Our approach provides a systematic way of performing fault diagnosis aspects of network fault management

Supervisory control of fuzzy discrete event systems with applications to mobile robotics

Fuzzy Discrete Event Systems (FDES) were proposed in the literature for modeling and control of a class of event driven and asynchronous dynamical systems that are affected by deterministic uncertainties and vagueness on their representations. In contrast to classical crisp Discrete Event Systems (DES), which have been explored to a sufficient extent in the past, an in-depth study of FDES is yet to be performed, and their feasible real-time application areas need to be further identified. This research work intends to address the supervisory control problem of FDES broadly, while formulating new knowledge in the area. Moreover, it examines the possible applications of these developments in the behavior-based mobile robotics domain. An FDES-based supervisory control framework to facilitate the behavior-based control of a mobile robot is developed at first. The proposed approach is modular in nature and supports behavior integration without making state explosion. Then, this architecture is implemented in simulation as well as in real-time on a mobile robot moving in unstructured environments, and the feasibility of the approach is validated. A general decentralized supervisory control theory of FDES is then established for better information association and ambiguity management in large-scale and distributed systems, while providing less complexity of control computation. Furthermore, using the proposed architecture, simulation and real-time experiments of a tightly-coupled multi-robot object manipulation task are performed. The results are compared with centralized FDES-based and decentralized DES-based approaches. -- A decentralized modular supervisory control theory of FDES is then established for complex systems having a number of modules that are concurrently operating and also containing multiple interactions. -- Finally, a hierarchical supervisory control theory of FDES is established to resolve the control complexity of a large-scale compound system by modularizing the system vertically and assigning multi-level supervisor hierarchies. As a proof-of-concept example to the established theory, a mobile robot navigation problem is discussed. This research work will contribute to the literature by developing novel knowledge and related theories in the areas of decentralized, modular and hierarchical supervisory control of FDES. It also investigates the applicability of these contributions in the mobile robotics arena

Composite Disturbance Filtering: A Novel State Estimation Scheme for Systems With Multi-Source, Heterogeneous, and Isomeric Disturbances

State estimation has long been a fundamental problem in signal processing and control areas. The main challenge is to design filters with ability to reject or attenuate various disturbances. With the arrival of big data era, the disturbances of complicated systems are physically multi-source, mathematically heterogenous, affecting the system dynamics via isomeric (additive, multiplicative and recessive) channels, and deeply coupled with each other. In traditional filtering schemes, the multi-source heterogenous disturbances are usually simplified as a lumped one so that the "single" disturbance can be either rejected or attenuated. Since the pioneering work in 2012, a novel state estimation methodology called {\it composite disturbance filtering} (CDF) has been proposed, which deals with the multi-source, heterogenous, and isomeric disturbances based on their specific characteristics. With the CDF, enhanced anti-disturbance capability can be achieved via refined quantification, effective separation, and simultaneous rejection and attenuation of the disturbances. In this paper, an overview of the CDF scheme is provided, which includes the basic principle, general design procedure, application scenarios (e.g. alignment, localization and navigation), and future research directions. In summary, it is expected that the CDF offers an effective tool for state estimation, especially in the presence of multi-source heterogeneous disturbances

Model based detection and reconstruction of road traffic accidents

This thesis describes the detection and reconstruction of traffic accidents with event data recorders. The underlying idea is to describe the vehicle motion and dynamics up to the stability limit by means of linear and non-linear vehicle models. These models are used to categorize the driving behavior and to freeze the recorded data in a memory if an accident occurs. Based on these data, among others the vehicle trajectory is reconstructed with fuzzy data fusion. The side slip angle which is a crucial quantity describing the vehicle stability is estimated with non-linear state observers and Kalman-Filters. The methodologies presented may lead from accident reconstruction considered here to accident avoidance

Review of Clustering Methods for Slow Coherency-Based Generator Grouping

Slow coherency is one of the most relevant concepts used in power systems dynamics to group generators that exhibit similar response to disturbances. Among the approaches developed for generator grouping based on slow coherency, clustering algorithms play a significant role. This paper reviews the clustering algorithms applied in model-based and data-driven approaches, highlighting the metrics used, the feature selection, the types of algorithms and the comparison among the results obtained considering simulated or measured data