Robust Tracking Control of Nonlinear Systems with Prescribed Performance

This paper proposes a sliding mode tracking control (SMC) approach for a class of state constrained nonlinear systems with prescribed transient and steady-state behavior. The prescribed tracking performance can be characterized by the inequalities on the output tracking error. The proposed SMC is designed based on a two-step backstepping procedure. At the first step, a virtual control scheme is designed by introducing and bounding an integral barrier function, by which the prescribed performance constraint and the system output constraint are satisfied. Then, the SMC is designed by introducing and bounding another integral barrier function, by which the control singularity problem is avoided and the state constraint is satisfied. Theoretical analysis and simulation results verify that the constraints is satisfied and the tracking error converges to an arbitrary small residual set, with convergence rate no less than a prescribed value, exhibiting a maximum overshoot less than a sufficiently small prescribed constant.

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