Input-Constrained Prescribed Performance Control for SISO Nonlinear Systems via Reference Relaxation

For a class of uncertain, single-input single-output (SISO) nonlinear systems, we consider the problem of prescribed performance tracking control under strict control input constraints. By prescribed performance, we mean that the system’s output should track a given reference signal, with an error confined within a user-prespecified time-varying envelope. The desired reference signal is also predefined by the user; however, when input saturation occurs, it is temporarily modified so that the tracking task becomes feasible given the provided level of saturation. With the proposed approach, it is proved that if the saturation level exceeds a given threshold that we explicitly quantity, then all closed-loop signals remain bounded and the desired reference can be tracked with arbitrary precision. Simulations verify and clarify theoretical results.