Abstract
This paper proposes a decentralised tracking control scheme for a class of nonlinear interconnected systems using sliding mode techniques. The desired output signals are time-varying. Both matched uncertainty and mismatched unknown interconnections are considered. Using geometric transformation, the considered system is transferred to a system with a unique structure to facilitate both the design of the sliding surface and the decentralised controllers. The sliding surface is designed based on the tracking error. A set of conditions are proposed to guarantee that when sliding motion occurs, the tracking errors converge to zero asymptotically while the system states are bounded. Decentralised controllers are then designed so that the interconnected systems' states can be driven to the designed sliding surface. Finally, simulation of a coupled inverted pendulum system demonstrates the results.
Highlights
Large-scale systems are often mathematically modelled by interconnections of a set of lower-dimensional subsystems
The designed systems should have a higher tolerance for the data-loss during data transformation, broken/unknown interconnections as well as poor communications to guarantee that the controlled large-scale systems have higher robustness
It should be emphasised that the results about output tracking for large-scale nonlinear interconnected systems with unknown interconnections are very few, when the ideal reference signals are time-varying
Summary
Large-scale systems are often mathematically modelled by interconnections of a set of lower-dimensional subsystems. Decentralized tracking control for large-scale systems is considered in [9] where model reference control is investigated. In [21], tracking problem for a class of large-scale systems with interconnections is considered using sliding mode control. It should be emphasised that the results about output tracking for large-scale nonlinear interconnected systems with unknown interconnections are very few, when the ideal reference signals are time-varying. Suitable coordinate transformations are introduced to transfer the nominal subsystems in the interconnected system to systems with special structure This makes each subsystem of the transferred system to separate into two parts to facilitate the system analysis and control design for output tracking. A decentralized sliding mode control scheme is proposed to drive the nonlinear interconnected systems to the designed sliding surface. The obtained results are applied to a river quality control to show the practicability and feasibility of the proposed approach
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