Global low-complexity hybrid tracking control of MIMO nonlinear systems with discontinuous references

This article explores the tracking control problem for strict-feedback multi-input multi-output (MIMO) nonlinear systems subject to deferred asymmetric output constraints, in the case where the reference signals are discontinuous. It strives not only to achieve discontinuous reference tracking without constraint violation, but also to actively damp error oscillations induced by external disturbances, unmodelled dynamics, and high-frequency references. The existing studies are limited to single-input single-output nonlinear systems, MIMO nonlinear systems with strong controllability conditions, or systems with available nonlinearities or reference derivatives. To overcome these limitations, a novel global low-complexity hybrid tracking control scheme consisting of a mixed-gain funnel constrained (FC) controller and a proportional-integral (PI) controller is put forward in this article. It retains the inherent simplicity of FC control and PI control, requiring neither function approximation, parameter identification, command filtering, nor disturbance estimation. Moreover, by inserting a shifting function and two parameters into the controllers, the proposed scheme helps alleviate the initial control peaking and enhances the transient performance of tracking errors. A two-link robotic manipulator example is provided to demonstrate the reliability of the developed control algorithm.