MODELING AND PERFORMANCE ANALYSIS FOR THE SERIAL AND PARALLEL PRODUCTION SYSTEM BASED ON GSPN

Differed from the existed applications of generalized stochastic Petri net(GSPN) theory in machine-tool manufacturing system, reliability computation of FMS, testabilityparameters determination and fault analysis, a new idea of applying GSPN to model and performanceanalysis for the serial and parallel production system is proposed. And one typical discrete eventdynamic system (DEDS), turner-unit of palletizing system, is taken as a real case to research. Basedupon the established GSPN models, the working performances of serial and parallel layout arecompared. Furthermore, their differences of working mechanisms including feeding mechanism,coordinating mechanism and monitoring mechanism are discussed. Thus the theoretical basis which ishelpful to appraise layout plan and its reasonableness is provided. Meanwhile, the research resultsshow that parallel layout is more advantageous to greatly improve the operational speed ofproduction system than serial one.

Modeling and Stability Analysis of a Communication Network System

In this work, the modeling and stability problem for a communication network system is addressed. The communication network system consists of a transmitter which sends messages to a receiver. The proposed model considers two possibilities. The first one, that messages are successfully received, while in the second one, during the sending process the transmitter breaks down and as a result the message does not reach the receiver. Timed Petrinets is the mathematical and graphical modeling technique utilized. Lyapunov stability theory provides the required tools needed to aboard the stability problem. Employing Lyapunov methods, a sufficient condition for stabilization is obtained. It is shown that it is possible to restrict the communication network system state space in such a way that boundedness is guaranteed. However, this restriction results to be vague. This inconvenience is overcome by considering a specific recurrence equation, in the max-plus algebra, which is assigned to the timed Petri net graphical model.

On the polynomial dynamic system approach to software development

In this paper the development of reactive software is transformed into a control problem, and the supervisory control theory for discrete event dynamic systems is suggested to solve this control problem. The operating environment under consideration is viewed as a controlled plant, the software under development as the corresponding controller, and the software requirements as the corresponding control objective. This idea leads to a constructive approach of software design, which ensures properties required a priori of the software under development. In this way the validation of the software under development is reduced to the validation of properties independent of implementation process. We reveal the inconsistence in using the concept of reachability to specify software requirements and clarify six different definitions of reachability. Two different definitions of invariance for specifying software requirements are also clarified. We then show how to synthesize the required controller or obtain software design solutions if the underlying software requirements are specified by several new combinations of reachability and invariance. The topic of this paper falls into the scope of software cybernetics that explores the interplay between software and control.

OBSERVABILITY OF EXTENDED TIMED EVENT GRAPH

In this paper, we study some results of extended timed event graph (ETEG)by using graph theory's methods in the dioid framework. A necessary and sufficient con-dition for the observability of ETEG is obtained and ETEG's standard structure is alsoestablished.

Supervisory Control of Extended Timed Event Graphs

Abstract This paper describes the dynamic behavior of extended timed event graphs related to place delay in the dioid framework. By Cofer and Garg's supervisory control theory^|3|, we address control problems of extended timed events graphs. Supervisory control of extended timed event graphs (a class of discrete event dynamic systems) is studied in the dioid framework, a necessary and sufficient condition for the ideals of the set of firing time sequences of transitions to be controllable is presented. We prove all the strongly controllable subsets can form a complete lattice.

Dynamic output feedback stabilization of deterministic finite automata via the semi-tensor product of matrices approach

This paper deals with the dynamic output feedback stabilization problem of deterministic finite automata(DFA).The static form of this problem is defined and solved in previous studies via a set of equivalent conditions.In this paper,the dynamic output feedback(DOF)stabilization of DFAs is defined in which the controller is supposed to be another DFA.The DFA controller will be designed to stabilize the equilibrium point of the main DFA through a set of proposed equivalent conditions.It has been proven that the design problem of DOF stabilization is more feasible than the static output feedback(SOF)stabilization.Three simulation examples are provided to illustrate the results of this paper in more details.The first example considers an instance DFA and develops SOF and DOF controllers for it.The example explains the concepts of the DOF controller and how it will be implemented in the closed-loop DFA.In the second example,a special DFA is provided in which the DOF stabilization is feasible,whereas the SOF stabilization is not.The final example compares the feasibility performance of the SOF and DOF stabilizations through applying them to one hundred random-generated DFAs.The results reveal the superiority of the DOF stabilization.

Complexity of comparing expressions in max-plus algebra

Max-plus algebra has been widely used in the study of discrete-event dynamic systems.Using max-plus algebra makes it easy to specify safety constraints on events since they can be described as a set of inequalities of state variables,i.e.,firing times of relevant events.This paper proves that the problem of solving max-plus inequalities in a cube(MAXINEQ)is nondeterministic polynomial-time hard(NP-hard)in strong sense and the problem of verifying max-plus inequalities(VERMAXINEQ)is co-NP.As a corollary,the problem of solving a system of multivariate max-algebraic polynomial equalities and inequalities(MPEI)is shown to be NP-hard in strong sense.The results indicate the difficulties in comparing max-plus formulas in general.Problem structures of specific systems have to be explored to enable the development of efficient algorithms.

Compatible-invariant subset analysis of deterministic finite automata via semi-tensor product of matrices approach

The compatible-invariant subset of deterministic finite automata（ DFA） is investigated to solve the problem of subset stabilization under the frameworks of semi-tensor product（ STP） of matrices. The concepts of compatibleinvariant subset and largest compatible-invariant subset are introduced inductively for Moore-type DFA,and a necessary condition for the existence of largest compatible-invariant subset is given. Meanwhile,by using the STP of matrices,a compatible feasible event matrix is defined with respect to the largest compatible-invariant subset.Based on the concept of compatible feasible event matrix,an algorithm to calculate the largest compatible-invariant subset contained in a given subset is proposed. Finally,an illustrative example is given to validate the results.