Input-Constrained Prescribed Performance Control for High-Order MIMO Uncertain Nonlinear Systems via Reference Modification

For a class of uncertain, multiple-input–multiple-output nonlinear systems, we consider the problem of prescribed performance tracking control under strict control input constraints. By prescribed performance, we mean that outputs of the system should track the given reference signals, with tracking errors confined within a user-specified performance envelope. However, as the controller imposing this desirable behavior is subject to inelastic control input constraints, the reference signals are temporarily modified whenever input saturation takes place, so that the tracking task becomes more feasible. It is proved that the proposed reference modification scheme leads to the exclusion of the internal instability phenomenon, from which conventional prescribed performance control suffers when subject to input saturation. In addition, it is proved that the proposed control architecture guarantees boundedness of all closed-loop signals given either an explicitly quantified feasibility condition on the saturation level, or provided that the system is input-to-state practically stable. Finally, the distortion of the reference signal owed to a possible saturation of the control input is quantified, and we additionally provide a level of saturation that can guarantee the reference signal will not be distorted, in the
$\mathcal {L}_\infty$
norm, more than a prespecified value. Simulation results verify and clarify theoretical findings.