A new Robust ‘Integral of Sign of Error’ feedback controller with adaptive compensation gain

In this paper, a new robust integral of signum of error (RISE) feedback type controller is designed for a class of uncertain nonlinear systems. Unlike the previous versions of RISE feedback type controllers, the proposed controller does not require prior knowledge of upper bounds of the vector containing the uncertainties of the dynamical system plus desired system dynamics (and their derivatives) for the control gain selection. The aforementioned enhancement is made possible via the design of a time-varying compensation gain as opposed to a constant gain used in previous RISE feedback type controllers. Asymptotic stability of the error signals and the boundedness of the closed-loop system signals are ensured via Lyapunov based arguments. Numerical simulation studies are presented to illustrate the viability of the proposed method.