Neural network algorithm for the synthesis of an optimal linear stochastic system with high availability according to the energy criterion

Paper is devoted to the problem of optimal neural network synthesis of linear stochastic system with high availability (StSHA) according to the energy criterion (EC). Such criterion means minimum of probabilistic second initial moment. One dimensional input signal being the sum of useful signal and Gaussian noise. Useful signal depends upon random parameters describing StSHA quality. Noise and random parameters are independent. In general case mathematical expectation of useful signal is not equal to zero. One dimensional output signal being the known transformation of useful signal. Architecture of 3 layer wavelet-neural network (WNN) with one reserved layer is developed. Activation function of reserved layer is defined using orthonormal wavelet basis compact carrier. For modeling of nonstationary stochastic processes (StP) canonical expansions based on WNN are implemented. For WNN functioning tutoring algorithm based on method of quick descend is used. Optimal synthesis operator according to EC is constructed in scalar and matrix form is constructed. Accuracy of EC optimal algorithm is estimated by error mathematical expectation and variance. Experimental software tools in MATLAB for StSHA quality analysis are designed and tested. Illustrated example convincing algorithm accuracy is presented. Basic conclusions and directions of future research are given.