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This article proposes a general approach to the simulation and design of a multilayer perceptron (MLP) network on the basis of cross-bar arrays of metal-oxide memristive devices. The proposed approach uses the ANNM theory, tolerance theory, simulation methodology and experiment design. The tolerances analysis and synthesis process is performed for the ANNM hardware implementation on the basis of two arrays of memristive microdevices in the original 16x16 cross-bar topology being a component of bidirectional adaptive neural interface for automatic registration and stimulation of bioelectrical activity of a living neuronal culture used in robotics control system. The ANNM is trained for solving a nonlinear classification problem of stable information characteristics registered in the culture grown on a multi-electrode array. Memristive devices are fabricated on the basis of a newly engineered Au/Ta/ZrO2(Y)/Ta2O5/TiN/Ti multilayer structure, which contains self-organized interface oxide layers, nanocrystals and is specially developed to obtain robust resistive switching with low variation of parameters. An array of memristive devices is mounted into a standard metal-ceramic package and can be easily integrated into the neurointerface circuit. Memristive devices demonstrate bipolar switching of anionic type between the high-resistance state and low-resistance state and can be programmed to set the intermediate resistive states with a desired accuracy. The ANNM tuning, testing and control are implemented by the FPGA-based control subsystem. All developed models and algorithms are implemented as Python-based software.