Robust Control of a Nonsmooth or Switched Control Affine Uncertain Nonlinear System Using a Novel RISE-Inspired Approach

For decades, nonlinear control methodologies have been developed to compensate for uncertain terms in the dynamical model that are upper bounded by constants. Classes of discontinuous and continuous controllers have been developed to compensate for these problematic terms; however, these controllers are prone to chatter or have been restricted to particular classes of uncertain and smooth nonlinear systems. Despite decades of research, an open question that remains is whether a chatter-mitigating control law can be developed to compensate for terms bounded by constants for a wider class of uncertain nonlinear systems, including switched or nonsmooth systems. To address this open question, this work considered a class of nonsmooth, uncertain, and control-affine nonlinear dynamic systems with an uncertain control effectiveness matrix. Furthermore, a novel filtered error, adaptive update law, and chatter-mitigating control law are developed to compensate for the uncertain control effectiveness matrix and the terms in the closed-loop error system that are bounded by constants. A nonsmooth Lyapunov-like stability analysis is performed to ensure semi-global exponential trajectory tracking to an ultimate bound.