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Schrödinger equation is a well known example of the so-called complex partial differential equations (C-PDE). This paper presents a technique based in the Differential Neural Networks (DNN) methodology to solve the nonparametric identification problem of systems described by C.PDE. In this case, the identification scheme is proposed as the composition of two coupled DNN: the first one is used to...
Observation problem for systems governed by Partial Differential Equations (PDE) has been a research field of its own for a long time. In this paper it is presented an observer design for a class or parabolic PDE's using sliding modes theory and bacstepping-like procedure in order to achieve exponential convergence. A Volterra-like integral transformation is used to change the coordinates of the error...
There are many examples in science and engineering which are reduced to a set of partial differential equations (PDE's) through a process of mathematical modeling. Nevertheless there exist many sources of uncertainties around the aforementioned mathematical representation. It is well known that neural networks can approximate a large set of continuous functions defined on a compact set to an arbitrary...
In this paper a strategy based on differential neural networks for the identification of the parameters in a mathematical model described by partial differential equations is proposed. The identification problem is reduced to finding an exact expression for the weights dynamics using the differential neural networks properties. The adaptive laws for weights ensure the convergence of the neural network...
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