Prescribed performance adaptive control of SISO feedback linearizable systems with disturbances

We consider the adaptive control problem for a class of SISO unknown nonlinear systems in the presence of additive input disturbances, with guaranteed prescribed performance. By prescribed performance we mean that the tracking error should converge to an arbitrarily predefined small residual set, with convergence rate no less than a prespecified value, exhibiting a maximum overshoot less than a sufficiently small prespecified constant. A novel output error transformation is introduced to transform the original "constrained" (in the sense of the output error restrictions) system into an equivalent "unconstrained" one. It is proven that stabilization of the "unconstrained" system is sufficient to solve the problem. The proposed robust adaptive controller is smooth and guarantees a uniform ultimate boundedness property for the transformed output error, plus the boundedness of all other signals in the closed loop. A simulation study on a Van der Pol system clarifies and verifies the approach.