Control of nonautonomous discrete event systems using dioid algebra

Multi-transitivity in non-autonomous discrete systems

Sensitivity of non-autonomous discrete dynamical systems

This paper focuses on chaos induced by weak A-coupled-expansion of non-autonomous discrete systems in compact subsets of metric spaces and in bounded and closed subsets of complete metric spaces, separately. A new concept of weak A-coupled-expansion for non-autonomous discrete systems, whose condition is weaker than that of A-coupled-expansion, is introduced, and several new criteria of chaos induced by weak A-coupled-expansion of non-autonomous discrete systems are established. By applying some close relationships between chaotic dynamical behaviours of the original system and its induced systems, two criteria of chaos are established. One example is provided for illustration.

On stability of nonlinear nonautonomous discrete fractional Caputo systems

The aim of this paper is to present some recent results concerning non-autonomous discrete systems (non-autonomous order one difference equations) and state some problems that arise in this field.

Bayesian optimal control for a non-autonomous stochastic discrete time system

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.

By using the variant fountain theorem, we study the existence of periodic solutions for a class of superquadratic non-autonomous second-order discrete Hamiltonian systems.

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.

Some weak versions of distributional chaos in non-autonomous discrete systems

Stable fiber bundles are the nonautonomous analogue of stable manifolds, and these objects provide valuable information on the underlying dynamics. We propose an algorithm for their computation that applies to a wide class of models, including noninvertible and nonautonomous discrete time systems. Precise error estimates are provided, and fiber bundles are computed for several examples.

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.

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

Due to the introduction of uncontrollable transitions in the supervisory control of discrete event systems modeled by controlled Petri nets, a disjunction of several linear inequalities is needed to express the admissible markings. In this paper, we propose a two level hierarchical control synthesis method to deal with this kind of OR logic constraints. In the method, the constraint function plays an important role not only in the construction of the low level monitor but also in the determination of the control policy. The obtained supervisor is maximally permissive and the online computation has the complexity of polynomial times. An example is used to illustrate the proposed synthesis algorithm.

In order to make it possible to effectively represent deterministic uncertainties and vagueness as well as the human subjective observation and judgement inherent to many real-world problems, especially those in biomedicine, we introduce, in this paper, fuzzy states and fuzzy events and generalize (crisp) discrete event systems (DES) to fuzzy DES. The largely graph-based current framework of the crisp DES is unsuitable for the expansion, and we have thus reformulated it using state vectors and event transition matrices which can be extended to fuzzy vectors and matrices by allowing their elements to take values between 0 and 1. To measure information related to fuzzy DES, we generalize the crisp DES observability. The new observability allows one to determine whether or not the system output observed is sufficient for decision making. Finally, we extend the optimal control of DES to fuzzy DES. The new fuzzy DES theory is consistent with the existing theory, both at the conceptual and the computation levels, in that the former contains the latter as a special case when the memberships must be either 0 or 1. Numerical examples are provided to illustrate the theoretical development.