Synthesis of a neural network control regulator of a nonlinear model of an inverted pendulum on a cart

In this article, we consider a method for selecting a structure of a neural network used to regulate an "inverted pendulum on a cart" object taking into account its additional features of a mathematical description, namely, nonlinear parameters. The algorithm is illustrated by the example of control synthesis which includes two neuroregulators. One of them is responsible for bringing the cart to the specified position, and the second is responsible for holding the pendulum in a vertical position. The structure transformations will be performed for the controller responsible for bringing the cart to the specified position. The architecture of a neural network controller is based on a discrete controller synthesized using polynomial matrix decomposition. For the original controller, we define the limits of its possible control of a nonlinear system. To increase the range of control of a nonlinear object, we perform transformations of the neural network structure of the original controller. We will make some complications in the structure of the neural network of the regulator, namely, increase the number of neurons and replace some activation functions with nonlinear ones (hyperbolic tangent). Next, we suggest one of the ways to select initial values of weight coefficients. Then we train the neural network and check the performance of the resulting controller on a nonlinear object. At the next stage, we compare the obtained performance of a controller having a complicated neural network structure with the performance of a classical controller. Thus, the purpose of this study is to formalize the synthesis procedure for a neural network controller for controlling a nonlinear object using a calculated classical controller for a linearized object model. The proposed method of generating the architecture of a neural network of controllers makes it possible to increase the range of control by a nonlinear object in comparison with the controller obtained by the method of polynomial matrix decomposition for a linear object. Compared to the typical ones, the proposed neural network structure is not redundant and therefore does not require additional computing resources to configure it.