Decentralised connectively finite-time control for a class of p-normal form nonlinear large-scale systems with expanding construction and its application.

In this paper, the decentralised connectively practical finite-time control problem is studied for a class of p-normal form large-scale systems with expanding construction. First, the decentralised connectively practical finite-time controllers are designed for the p-normal form large-scale systems without expanding construction by combining adding a power integrator technique, the backstepping method, the Lyapunov theory with the neural adaptive technology. The designed controllers can guarantee that all the signals of the closed-loop system are practically finite-time stable and the large-scale system is connectively stable. Then, the expansion of the system is considered. A new subsystem is added to the original system online. It is needed that the decentralised control laws and the adaptive laws of the original system are kept to be unchanged, and only the control laws and the adaptive laws for the newly added subsystem need to be designed. Under the premise, the control laws and the adaptive laws of the new subsystem are designed, which can guarantee that both newly added subsystem and resultant expanded closed-loop large-scale system are connectively practically finite-time stable. The singularity problem arising in the design process for practical finite-time control is solved. Here, the adding a power integrator technique is applied to handle the control design problem for p-normal form systems. And the control laws and the adaptive laws are simplified by neural networks. The two numerical examples including an actual double-inverted pendulum system connected by a spring are presented to show the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]