Adaptive Neural-Network-Based Control of Nonlinear Underactuated Plants: An Example of a Two-Wheeled Balancing Robot

Abstract. This paper proposes a new method to control nonlinear underactuated plants for eliminating unmatched parametric uncertainties. The method is based on a model reference adaptive control. The controller consists of a basic LQ one and an adaptive compensator reducing the uncertainty norm under certain assumptions. The compensator involves a multilayer neural network due to its universal approximation properties. The network is trained online. The equations to tune the compensator’s neural network parameters are derived using Lyapunov’s second method and the backpropagation algorithm. The asymptotic convergence of the tracking error (the difference between the plant’s and reference model’s outputs) to a given domain is proved. The theoretical results are validated by numerical experiments with the developed control system for the mathematical model of a balancing LEGO EV3 robot in MATLAB.

Keywords: model reference adaptive control, balancing robot, suppression of unmatched parametric uncertainties, neural networks, online training, stability.

Funding. This work was partially supported by the Russian Foundation for Basic Research, project no. 18-47-310003-r_a.