Abstract
The modeling of dynamic systems is frequently hampered by a limited knowledge of the system to be modeled and by the difficulty of acquiring accurate data. This often results in a number of uncertain system parameters that are hard to incorporate into a mathematical model. Thus, there is a need for modeling formalisms that can accommodate all available data, even if uncertain, in order to employ them and build useful models. This paper shows how the Flexible Nets (FNs) formalism can be exploited to handle uncertain parameters while offering attractive analysis possibilities. FNs are composed of two nets, an event net and an intensity net, that model the relation between the state and the processes of the system. While the event net captures how the state of the system is updated by the processes in the system, the intensity net models how the speed of such processes is determined by the state of the system. Uncertain parameters are accounted for by sets of inequalities associated with both the event net and the intensity net. FNs are not only demonstrated to be a valuable formalism to cope with system uncertainties, but also to be capable of modeling different system features, such as resource allocation and control actions, in a facile manner.
Highlights
The development of appropriate models is crucial for the design, analysis and control of dynamic systems
This paper exploits the particular features of Flexible Nets (FNs), a modeling formalism introduced in Julvez et al (2018) to study Wilson disease, to model and analyze dynamic systems with uncertain parameters, to account for partially observable systems and, to compute the control actions that optimize a given control objective
This section introduces Flexible Nets (FNs), which can be denoted as P H T nets, i.e. places P and transitions T are connected by event and intensity handlers
Summary
The development of appropriate models is crucial for the design, analysis and control of dynamic systems. Let us further assume that the rate of reaction R1 is uncertain, but constrained to the interval [4.5, 5.5], i.e. the number of reactions that occur per time unit is in [4.5, 5.5], and the rate R2 satisfies 0.9[A] ≤ rate(R2) ≤ 1.1[A], i.e. it is proportional to [A] with an uncertainty of 10% These reaction rates are modeled in the FN by the inequality associated with R1 and the inequality associated with the dot labelled s1 (which will be denoted intensity handler). The evolution of continuous Petri nets (Silva et al 2011), which can be seen as a relaxation of Petri nets (Murata 1989), is determined by a set of ordinary differential equations Another popular modeling formalism that can graphically represent systems in different domains and that can be converted to state space representation is bond graphs (Borutzky 2010).
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