This paper develops a neural network architecture and a new processing method for solving in real time, the nonlinear equality constrained multiobjective optimization problem (NECMOP), where several nonlinear objective functions must be optimized in a conflicting situation. In this processing method, the NECMOP is converted to an equivalent scalar optimization problem (SOP). The SOP is then decomposed into several-separable subproblems processable in parallel and in a reasonable time by multiplexing switched capacitor circuits. The approach which we propose makes use of a decomposition-coordination principle that allows nonlinearity to be treated at a local level and where coordination is achieved through the use of Lagrange multipliers. The modularity and the regularity of the neural networks architecture herein proposed make it suitable for very large scale integration implementation. An application to the resolution of a physical problem is given to show that the approach used here possesses some advantages of the point of algorithmic view, and provides processes of resolution often simpler than the usual techniques.

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In this paper, we show a neural network implementation in fixed time of adjustable order statistic filters, including sorting, and adaptive-order statistic filters. All these networks accept an array of N numbers Xi = S(Xi)M(Xi)2E(Xi) as input (where S(Xi) is the sign of Xi, M(Xi) is the mantissa normalized to m digits, and Ex is the exponent) and employ two kinds of neurons, the linear and the threshold-logic neurons, with only integer weights (most of the weights being just +1 or -1) and integer threshold. Therefore, this will greatly facilitate the actual hardware implementation of the proposed neural networks using currently available very large scale integration technology. An application of using minimum filter in implementing a special neural network model neural network classifier (NNC) is given. With a classification problem of l classes C1, C2,.. ., C1, NNC classifies in fixed time an unknown vector to one class using a minimum-distance classification technique.

Due to the low total cost of production, Photovoltaic energy constitutes an important part of the renewable energy installed in the world. However, photovoltaic energy is volatile in nature because it depends on weather conditions, which makes the integration, control and exploitation of this type of energy difficult for grid operators. In the traditional grid architecture, system operators have accumulated enough experience that enables them to determine how much operating reserves are required to maintain system reliability based on statistical tools. Still, with the introduction of renewable energy (wind and photovoltaic), the grid structure has changed, and to maintain grid stability, it is becoming fundamental to know renewable energy state and production that can be combined with other less variable and more predictable sources to satisfy the energy demand. Therefore, renewable energy forecasting is a straightforward way to integrate safely this kind of energy into the current electric grid, especially photovoltaic power forecasting, which is still at a relative infancy stage compared to wind power forecasting, which has reached a relatively mature stage. The goal of this work is to present, first, a short-term offline forecasting model that uses only in-situ (local) collected data. Also, the performances of several pure non-linear auto-regressive models are investigated against those of non-linear auto-regressive models with exogenous inputs. For this purpose, two well-known statistical learning techniques, namely Feed Forward Neural Network and Least Square Support Vector Regression, have been used. To test the performance of the models, the results obtained are compared with those of a benchmark model. In this paper, we used the persistent model as well as a multivariate polynomial regression model as benchmark.

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