System structure based decentralized sliding mode output tracking control for nonlinear interconnected systems

In this article, a decentralized tracking control scheme is proposed for a class of nonlinear interconnected systems with uncertainties using sliding mode technique. Both matched nonlinear uncertainty and mismatched known nonlinear interconnections are considered. Under the condition that the nominal isolated subsystems have relative degrees, a geometric transformation is applied to transfer the interconnected system into a new nonlinear interconnected system with a special structure to facilitate the system analysis and design. Then, a composite sliding surface is designed in terms of tracking errors, and decentralized controllers are proposed to drive the system states to the designed sliding surface in finite time and maintain a sliding motion on it thereafter. A set of conditions are developed to guarantee that the output tracking errors converge to zero asymptotically while all system state variables are bounded. The considered interconnected systems are nonlinear and it is not required that either the isolated subsystems or the isolated nominal subsystems are linearizable. The desired output signals are allowed to be time-varying. Finally, the developed results are applied to an inverted coupled-pendulum system. Simulation demonstrates that the proposed control scheme is effective.