Constraint function based hierarchical control of discrete event systems

Hierarchical Multitasking Control of Discrete Event Systems: Computation of Projections and Maximal Permissiveness

This paper proposes a solution to the electric Vehicle Scheduling Problem (eVSP) based on the framework of Discrete Event System (DES). A supervisory control is synthesized using the theory of Supervisory Control of Discrete Event System (SCDES) to manage the power admission control of a group of local Plug-in Electric Vehicles (PEV). The PEVs are categorized based on their level of priority to be charged and an algorithm is developed to allocate power to PEVs according to their priority and available capacity. The proposed algorithm and supervisor validates the schedulability of charging of PEVs while meeting the constraint of the grid to achieve peak demand reduction. Simulation studies are carried out using MATLAB/Simulink and STATEFLOW toolkit and the result validates the effectiveness of the control scheme to reduce peak demand while providing fair charging schedules to PEVs.

We propose a formalism for decentralized control of discrete event systems with communications. The formalism is based on PN/sup 2/, a class of agent-oriented Petri nets proposed by the author (2001). The main difference between PN/sup 2/ and Petri nets is that each token, representing an agent, is also a Petri net. The decentralized control system to be modeled has the following features: (1) the system is asynchronous and has no global clock; (2) some events may occur concurrently; (3) the system is controlled by several control agents, each of which perceives only a subset of occurring events, and can control only a subset of events; and (4) each control agent can communicate with other agents. By communications, each agent can know occurrences of events that are not observable for it, and can ask other agents to disable events that are not controllable for it. Using the formalism, we define a problem concerning control synthesis.

In this paper a hybrid approach is proposed for supervisory control of discrete event systems (DES) subject to forbidden states. Assuming that an uncontrolled bounded Petri net (PN) model of a (plant) DES and a set of forbidden state specifications are given, the proposed approach computes a maximally permissive and nonblocking closed-loop hybrid model. The first step is to simplify the given PN model by means of PN reduction rules. The simplified model and the specifications are then represented as buffers, and supervisory control theory (SCT) is applied to obtain a Ramadge–Wonham (RW) supervisor in the form of an automaton. After reduction of the latter’s state size by a ‘control congruence’, the simplified RW supervisor is represented by a so-called auto-net and coupled to the given uncontrolled PN plant model by means of inhibitor arcs to represent the disabling actions. The plant model and supervisor auto-net run concurrently, synchronizing on shared events. This procedure provides a maximally permissive and nonblocking ‘hybrid’ (mixed PN/automaton) closed-loop controlled system. The method is straightforward logically, graphically, and technologically. Its applicability is shown by two examples, one of them a workcell from the PN control literature.

A modified normality condition for decentralized supervisory control of discrete event systems

In decentralized control of discrete event systems, two main agents contribute to the computation of decisions: local supervisors and fusion modules. The local supervisors process the information detected on the plant and its environment, and transmit their results to the fusion modules. The latter process what is received from the local supervisors in order to decide actions to be applied to the plant. In the existing decentralized control architectures, the local supervisors execute complex operations, while the fusion modules execute simple operations. In the present article, we propose to move the decision computation complexity from local supervisors to fusion modules, that is what we term: moving decisions closer to actions. We justify this movement of decision and develop a simple architecture based on it. With the proposed architecture, the local supervisors are simple local observers, while all decisions are computed by the fusion modules. We characterize the class of languages achievable with the new architecture and compare it with the classes of languages achievable with the existing decentralized architectures and the centralized architecture.

A new hierarchical coordination controller is proposed for large scale discrete event systems. A control task is decomposed into several independent subtasks and a coordinator is constructed so as to control the lower level supervisors in the form of supervisor conjunction. Necessary and sufficient conditions for the existence of this coordinator are derived, and a construction procedure is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Petri nets have been extensively applied for specification, design, verification, performance evaluation, and simulation of discrete event control systems (DECS). The usual way to verify the dynamic behaviour of DECS design is to employ a process-based model, which proves to be impractical in application because the process-based model does not usually fully correspond to the control programming behaviour. This paper proposes a sensor-based stage Petri net (SBSPN) to represent a programmable logic controller (PLC) stage logic diagram (LD) for discrete-event control design. The new technique is able to simplify the modelling process of the complex PLC program without considering the interlocking problem within the ladder diagram. An illustrated example is used to explore the new methodology. The proposed method contains the power and flexibility of the Petri net analysis prior to the PLC implementation. It is believed that this technique is significant for industry practice.

Analysis and control of fuzzy discrete event systems using bisimulation equivalence

For over twenty years, hybrid systems, involving both a discrete-valued state component and a continuous-valued state component (evolving in either discrete or continuous time), have challenged control engineers interested in expanding the applications of control theory. In particular, the hybrid system representation has motivated the formulation of "fault-tolerant" optimal control problems for systems subject to abrupt changes in their structure, parameters or operating environment. One approach has been the development of optimal controllers for jump linear systems. Strong theoretical results are currently limited, however, to Markov and semi-Markov jump processes, when change in the system structure are perfectly observed. During the same two decades, theory and methods for the analysis of discrete event systems have been developed. Recently the control of discrete event systems has received significant attention. This paper is directed toward the application of jump systems control theory to the control of continuous variable processes driven by discrete event systems.

Towards Optimal Supervisory Control of Probabilistic Discrete Event Systems

We investigate modeling and control of probabilistic fuzzy discrete event systems (PFDES). PFDES is a new type of fuzzy discrete event systems. It allows the use of probabilities to describe the chances of occurrences of different events. Our new model for PFDES consists of a fuzzy automaton and a crisp automaton that specifies what sequences of events can occur and their probabilities of occurrences. Based on the new model, optimal control is designed using an on-line and limited lookahead method. Control is calculated one step at a time, after an occurrence of an event. At each step, a lookahead window of $N$ events is constructed. The performance measures for all states in the window are determined, which is a function of fuzzy states. Control is calculated to maximize the expected performance measure after the occurrences of $N$ events. To reduce computational complexity, a “dynamic-programming” approach is proposed. We prove that the control obtained is optimal. Examples are given in the paper to illustrate the results.

A stochastic optimization problem for discrete event dynamic systems is addressed and solved by means of concurrent estimation and ordinal comparison. A performance function defined on the system must be optimized by choosing an appropriate resource allocation. An analytical expression of the objective function is not available, and concurrent estimation is used to estimate it. The approach proposed in this paper, which can be applied more easily than the methods presented previously, exploits the fast convergence rate of order statistics in order to reduce computation effort.

Supervisory control of discrete event systems under asynchronous spiking neuron P systems

Discrete event systems (DESs) are powerful abstract representations for large human-made physical systems in a wide variety of industries. Safety control issues on DESs have been extensively studied based on the logical specifications of the systems in various literature. However, when facing the DESs under uncertain environment which brings into the implicit specifications, the classical supervisory control approach may not be capable of achieving the performance. So in this research, we propose a new approach for optimal control of DESs under uncertain environment based on supervisory control theory (SCT) and reinforcement learning (RL). Firstly, we use SCT to gather deliberative planning algorithms with the aim to safe control. Then we convert the supervised system to Markov Decision Process simulation environments that is suitable for optimal algorithm training. Furthermore, a SCT-based RL algorithm is designed to maximize performance of the system based on the probabilistic attributes of the state transitions. Finally, a case study on the autonomous navigation task of a delivery robot is provided to corroborate the proposed method by multiple simulation experiments. The result shows the proposed approach owning 8.27%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} performance improvement compared with the non-intelligent methods. This research will contribute to further studying the optimal control of human-made physical systems in a wide variety of industries.