Analytic Calculus of Response Time in Networked Automation Systems

One of the main concerns about implementing networked automation systems is ensuring its security against cyber attacks. In this paper, we consider networked automation systems abstracted as Discrete-Event Systems (DES), and consider cyber attacks where a malicious agent eavesdrops a network communication channel with the objective to gather information about the system behavior. It is important to remark that network security strategies used in Information Technology (IT) cannot be straightforwardly used in industrial networks, since the control of automation systems usually requires small communication delays, which limits the size of the data that can be transmitted in the communication network. In this paper, we introduce a new cryptographic scheme based on events, called event-based cryptography, where an event is defined as any change in the binary signals transmitted in the channel. We also present a necessary and sufficient condition that the event-based encryption function must satisfy to be used in the cryptographic scheme proposed in this paper, and present a class of encryption functions that can be modeled by Mealy automata. We also present procedures for the implementation of the event-based encryption function, and illustrate all results with a practical example.

The ongoing integration of various devices and services into nowadays buildings as part of networked building automation systems (BAS) demands for flexible and dynamically adaptable system architectures as they are supported by service orientation, which, moreover, can provide suitable abstractions when integrating new technologies and systems arising for example from the Internet of Things. The increasing complexity of such service systems, however, is accompanied by increasing dependability requirements. Therefore a comprehensive and automated technical management system including service lifecycle management, dynamic (re-)configuration, distributed (re-)deployment, self-repair etc. has to be accomplished. Furthermore the management tasks and the required abstraction of the managed system should span a defined state space in order to enable formal verification of system characteristics like dependability. This work reports on a technical management system utilizing general and system-specific event-condition-action-rules (ECA rules) to enable the dependable operation of BAS. The management tree does not only serve as homogeneous management interface to the BAS, but spans in conjunction with the ECA rules the desired state space.

This chapter discusses the timed event graphs (TEGs) a suitable tool for the modelling of manufacturing systems characterized by synchronization and delay phenomena but devoid of choices. Furthermore, TEGs have a linear representation in an algebraic structure called idempotent semirings. The chapter introduces several idempotent semirings, for example, max-plus algebra min-plus algebra and minax and demonstrates with several examples. As many manufacturing systems and the operation are subject to additional constraints, the standard notion of linear systems in dioids has been extended. Using the approach, it is possible to model minimal and maximal operation times, that is, time window constraints, as well as minimal and maximal numbers of work in progress, for example, in systems operating with a nested schedule. The chapter shows that the approach is relatively robust to mistakes in the modelling procedure. More precisely, if unfeasible constraints are requested, the resulting system will indicate that some transitions are blocked from the beginning.

This article deals with the analysis of discrete event systems which can be modelled by timed event graphs with multipliers (TEGMs). These graphs are an extension of weighted T-systems studied in the Petri net literature. These models do not admit a linear representation in (min, +) algebra. This nonlinearity is due to the presence of weights on arcs. To mitigate this problem of nonlinearity and to apply some basic results used to analyse the performances of linear systems in dioid algebra, we propose a linearisation method of mathematical model reflecting the behaviour of a TEGM in order to obtain a (min, +) linear model.

PROBABILISTIC HYBRID AUTOMATA WITH VARIABLE STEP WIDTH APPLIED TO THE ANAYLSIS OF NETWORKED AUTOMATION SYSTEMS

Modeling and analysis of discrete-event dynamic systems representing manufacturing processes are considered. The manufacturing processes considered represent the repetitive production of a given number of products by means of a fixed set of machines. It is necessary to introduce a certain number of simplifying assumptions to make the system representable by timed event graphs, a special class of Petri nets, for which tools capable of providing an analytical performance evaluation exist. In this framework, some analysis and optimization problems can be considered. >

This contribution addresses the estimation problem of holding times in timed event graphs. Based on the known Petri net topology the holding times are determined such that an equation error is minimized. The paper investigates the important issue of convergence of the estimated parameters to the true parameter values and shows that this objective can be achieved by applying particularly chosen input signals. A new iterative estimation procedure is proposed using these suitably designed input signals.

The class of Discrete Event Systems which can be modelled as timed event graphs may be described by linear equations in a non-traditional algebraic systems called a dioid or max-algebra. This paper extends the dioid algebra approach to a broader class of systems including both timed and untimed models, time-varying systems, and decision-making systems. We introduce an algebraic structure called a dioid vector space which allows any number of continuous functions to be included in the system description.

Localization of time shift failures in (max,+)-linear systems

This paper proposes and analyzes an efficient robot task sequence for a flexible assembly system that consists of multiple 3D printers, post-processing, assembly, inspection machines, and a material handling robot. The flexible assembly system, which has been built in many large cities in Korea, has been designed to fabricate customized products for start-ups or individuals. We consider cyclic scheduling of the system in which the robot repeats a certain sequence to produce identical products. We propose a robot task sequence to minimize the cycle time. The system behavior with the proposed robot task sequence is modeled with a timed event graph (TEG), and the optimality of the sequence is proved by analyzing the circuits in the TEG. The results are extended for producing multiple types of products simultaneously.

The class of timed event graphs (TEGs) has widely been studied thanks to an approach known as the theory of max-plus linear systems. In particular, the modeling of TEGs via formal power series in a dioid called Min <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ax</sup> [[ γ,δ]] has led to input-output representations on which some model matching control problems have been solved. Our work attempts to extend the class of systems for which a similar control synthesis is possible. To this end, a subclass of timed Petri nets that we call weight-balanced timed event graphs (WBTEGs) will be first defined. They can model synchronization and delays (WBTEGs contain TEGs) and can also describe dynamic phenomena such as batching and event duplications (unbatching). Their behavior is described by rational compositions (sum, product and Kleene star) of four elementary operators γ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> , δ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sup> , μm, and βb on a dioid of formal power series denoted ε* [[ δ]]. The main feature is that the transfer series of WBTEGs have a property of ultimate periodicity (such as rational series in M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ax</sup> [[ γ,δ]]). Finally, the existing results on control synthesis for max-plus linear systems find a natural application in this framework.

Timed event graphs (TEGs) are a subclass of timed Petri nets suitable to model decision-free timed discrete event systems. In classical TEGs, exact synchronization of two transitions T1 and T2 is available by requiring that transitions T1 and T2 fire simultaneously. In this paper, a new sort of synchronization, namely partial synchronization, is introduced: transition T2 has to fire when transition T1 fires, but transition T1 is not influenced by transition T2. Under some assumptions, optimal control, already available for classical TEGs, is extended to TEGs under partial synchronization.

In this paper, the aim is to make the predictive control of a plant described by a Timed Event Graph which follows the specifications defined by a P-time Event Graph. We propose a compromise approach between the ideal optimality of the solution and the on-line application of the computed solution when the relevant optimal control cannot be applied for a given computer. The technique is based on a reduction of the number of iterations of the fixed point algorithm such that the computed control remains causal. The analysis of the partial satisfaction of the specifications at each iteration of the algorithm defined in the (max, + ) algebra shows that a subset of constraints is guaranteed by the control computed at each iteration while another one is possibly satisfied.

The paper describes a novel approach to model any deterministic manufacturing system. A function block diagram type of model is proposed. A block can be a single machine or a factory. The model is expressed as a system of linear event timing equations using max-plus algebra. One of the advantages of block diagram representation is the simplicity of algebraic relations between the sub-system transfer functions [1]. It is expected that the proposed model will make it possible to develop and use techniques similar to those found in classical transfer function block diagrams.

It is well known that the modeling issues in Dynamical systems in chemical processes, networked control systems and automation systems are very complex and model may contain subsystems with different delays. Because of the mathematical complexity, the robust control of these types of multiple time delay system is a challenging one. The problem becomes more difficult and complex when the system is having time delays in both the denominator and the numerator. In this paper a new method is proposed for approximating general multiple time delay continuous-time transfer function system with multiple time delays in both the denominator and the numerator to a single input/output delay. Both Single Input Single Output(SISO) and Multi Input Multi Output(MIMO) cases have been considered. In this proposed methodology, the Approximated Generalized Time Moments (AGTM)/ Approximated Generalized Markov Parameter (AGMP) methods are used to transform the multiple time delay system into a single input/output delay system. A Linear Matrix Inequality (LMI) approach is developed for synthesizing robust H∞ control of the approximated time delay system. The efficacy of the proposed method is shown through illustrative examples. It is evident from the simulation results that the approximated system is stable with the proposed LMI H∞ controller.