Lech Jamroż

The following article presents the application of the Max-Plus Linear System (MPLS) method in the synthesis of different IT process control structures, taking place in the systems belonging to the class of Discrete Event Systems (DES). Modelling and analysis of these systems are based on the state equations, expressed in MPLS categories and classical principles of control theory, adapted for them. MPLS is based on max-plus algebra formalism and is supported with graphical representation in the form of Timed Event Graph (TEG), which is the special case of Timed Petri Nets (TPN). The article contains an overview of the theoretical work on discrete control processes, with a particular focus on the synthesis of control signals in the open control to obtain the desired output system. A practical example has been used for distributed computational process and data transmission for the system controlling selected technological process. Numerical results are presented.

The increasing complexity of information processing in distributed computer systems and microprocessors requires the use of time-saving devices and extended capacities of transmission channels. Processes in computers systems need effective processing time. This article describes an application of the theory of the Max Plus Linear System (MPLS) to controlling digital information processing and transmission time in information systems. System processes are described by an MPLS state equation and an MPLS output equation. The MPLS model makes use of formal mathematical methods of max-plus algebra which include maximization and addition operations in the domain of non-negative real numbers with the addition of minus infinity. The input data and the structure of the processes under consideration are represented by the Timed Event Graph (TEG) formalism constituting a special case of Timed Petri Nets. The suggested MPLS methods are useful for investigating selected properties of network models. They may be applied, among others, to evaluate performance criteria, cycle time, predictive control etc. This article presents the theoretical considerations used to determine the input signals controlling discrete processes, which are then illustrated with examples of numerical computations.

This article relates to a synthesising output feedback that is used to control a network of discrete events. The feedback stabilises the system without reducing its initial throughput and its synthesis is mainly based on the theory of residues and the Kleene operator. This article suggests some theoretical results and mathematical foundations of max-plus algebra theory, and in particularly, discusses various other aspects of controlling discrete processes and their modelling in the context of a linear max-plus system.