NEURAL NETWORK OPTIMIZATION OF AREAS OF EXISTENCE OF THE SLIDING MODE ON THE BASIS OF QUALITATIVE ANALYSIS OF PHASE SPACE PROJECTIONS

Abstract

The paper proposes a method for neural network optimization of the regions of existence of a sliding mode in the projections of the phase space of a control object for the purpose of subsequent synthesis of control systems with sliding modes. Expanding the regions of existence of a sliding mode provides greater freedom in choosing sliding surfaces, including nonlinear ones, and allows us to expect an improvement in the quality of control. The purpose of the study is to determine the applicability of modern machine learning methods, in particular neural networks and genetic algorithms, in problems of optimizing the regions of existence of a sliding mode using the example of a 4th order nonlinear system. Materials and Methods. To solve the problem, numerical methods of machine learning of neural networks and stochastic directed search, in particular, genetic algorithms, are used. A method for analyzing particular two-dimensional projections of the phase space of a multidimensional system is also used. Results. A structural classification of phase space projections with neural network optimization of the regions of existence of a sliding mode is proposed to ensure automated synthesis of control algorithms. The paper considers the features of phase space projections of multidimensional systems using a fourth-order pulse converter as an example. It proposes a method for constructing switching lines for a sliding mode based on phase space projections, which allows classifying projections in terms of their suitability for organizing control in a sli-ding mode. The sliding mode existence regions are maximized using a stochastic genetic algorithm and a neural network in the form of a multilayer perceptron. The network is implemented using the TensorFlow library for constructing and training neural networks. The Adam optimizer is used to update the model. It is shown that optimization using a genetic algorithm and a neural network allows for a significant increase in the potential for selecting control algorithms by expanding the sliding mode existence regions in phase space projections. Conclusion. The results of the application of the genetic algorithm and training of a multilayer neural network demonstrate that the proposed method expands the scope of application of phase space projections in problems of synthesis of control of multidimensional nonlinear systems and opens up new possibilities for increasing the efficiency of control in sliding modes.