Control of time-delay interconnected nonlinear systems under input saturations: a broad learning system-based approach

In this paper, the adaptive control problem is investigated for a class of interconnected nonlinear systems (INS) with unknown interconnection delays and input saturations. For state unmeasurable problem, a full dimension state observer (SO) is designed to estimate the inaccessible state variables. Broad learning system (BLS), a novel nonlinear approximation technique, is introduced in this study to identify the unknown dynamics and could achieve better approximation performance. An adaptive distributed control (DC) scheme is proposed for the uncertain time-delay INS without input saturation, which guarantees that the stability of the closed loop INS. On this basis, the input saturation problem is further considered, an online approximation smooth function is added into the distributed adaptive tracking controller, such that the closed-loop INS have the anti-input saturation capability. In terms of Lyapunov theory, all the signals in the closed-loop uncertain time-delay INS with input saturation are proved to be uniformly ultimately bounded (UUB) and the tracking errors could converge to a small neighbourhood of zero. Finally, one simulation example performed on two parallel inverted pendulum cars demonstrates the superiority of the developed distributed control scheme.