Neural-Based Decentralized Robust Control of Large-Scale Uncertain Nonlinear Systems with Guaranteed H<sub>∞</sub> Performance

Abstract

This paper investigates an application of neural networks (NNs) to the decentralized guaranteed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance for a class of large-scale uncertain nonlinear systems. In order to guarantee the adequate H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance level for the nonlinear systems, nonlinear linear matrix inequality (NLMI) condition is derived. The linear matrix inequality (LMI) approach instead of the NLMI is used to construct the decentralized local state feedback controllers with additive gain perturbation. The novel contribution is that in order to avoid H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance degradation caused by the uncertainty, NNs are substituted into the additive gain perturbations. Although the NNs are included in the large-scale uncertain nonlinear systems, it is newly shown that the closed-loop system is internally stable and the adequate H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance bound is attained. Finally, a numerical example is given to verify the efficiency