Adaptive Decentralized Control for Constrained Strong Interconnected Nonlinear Systems and Its Application to Inverted Pendulum

This work is dedicated to adaptive decentralized tracking control for a class of strong interconnected nonlinear systems with asymmetric constraints. Currently, there are few related studies on unknown strongly interconnected nonlinear systems with asymmetric time-varying constraints. To deal with the assumptions of the interconnection terms in the design process, which include upper functions and structural restrictions, the properties of Gaussian function in radial basis function (RBF) neural networks are applied to overcome this difficulty. By constructing the nonlinear state-dependent function (NSDF) and using a new coordinate transformation, the conservative step that the original state constraint converts into a new boundary of the tracking error is removed. Meanwhile, the virtual controller's feasibility condition is removed. It is proven that all the signals are bounded, especially the original tracking error and the new tracking error, which are both bounded. In the end, simulation studies are carried out to verify the effectiveness and benefits of the proposed control scheme.