A self tuning RISE controller formulation

In recent years, controller formulations using robust integral of sign of error (RISE) type feedback have been successfully applied to a variety of nonlinear dynamical systems. The drawback of these type of controllers however, are (i) the need of prior knowledge of the upper bounds of the system uncertainties and (ii) the absence of a proper gain tuning methodology. To tackle the aforementioned weaknesses, in our previous work [1] we have presented a RISE formulation with a time-varying compensation gain to cope for the need of upper bound of the uncertain system. In this study, we have extended our previous design to obtain a fully self tuning RISE feedback formulation. Lyapunov based arguments are applied to prove overall system stability and extensive numerical simulation studies are presented to illustrate the performance of the proposed method.