Prescribed Performance Control for Discontinuous Output Reference Tracking

This article considers the problem of prescribed performance tracking control for a class of uncertain, multi-input multi-output (MIMO) nonlinear systems having a low-triangular structure, with possibly discontinuous reference signals. Prescribed performance means that the output tracking errors should converge to a prescribed maximum residual set in fixed time, exhibiting a predefined maximum overshoot. The controller we propose is of low complexity and is designed according to the philosophy of the prescribed performance control (PPC) methodology. However, significant modifications on the standard PPC design are provided to successfully handle the presence of discontinuities in the reference. Key characteristic is the incorporation of impulsive dynamics in the control design, leading to an impulsive closed-loop system. Knowledge of neither the future values of the reference signal nor the time instants of the reference discontinuities is required. Simulation results clarify and verify theoretical findings.