Supporting CPS modeling through a new method for solving complex non-holomorphic equations

Masetti G., Dutto S., Chiaradonna S., Di Giandomenico F.

Wirtinger derivatives  Newton-raphson  Non-holomorphic functions  Generative Programming  Complex system of equations 

Modeling cyber-physical systems (CPSs) for assessment or design support purposes is a complex activity. Capturing all relevant physical, structural or behavioral aspects of the system at hand is a crucial task, which often implies representation of peculiar features/constraints through non-linear equations. Values that fulfill the constraints, described with a domain specific language, are obtained solving the equations through a properly developed solution tool. Only for a limited set of CPSs it is possible to find a straightforward strategy to design the software that solves the constraints equations. In the general case, instead, the modeler has to develop an ad-hoc artifact for each different system. This is the case of non-holomorphic but real analytic complex equations, adopted to represent system components with wave behaviors. In this paper, we present a new approach to develop a software for solving such complex equations following a generative programming strategy, based on Wirtinger derivatives within the Newton-Raphson method.

Source: 6th International Conference on Model-Driven Engineering and Software Development, MODELSWARD, pp. 680–688, Madeira, Portugal, 22-24 January, 2018

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