###### Abstract  
To deal with uncertainties in a dynamic system, many nonlinear control approaches have been considered. Unique challenges arise from uncertainties that are bounded by constants, which has led to the development of both continuous and discontinuous control methods. However, these methods either are limited to classes of smooth nonlinear models or have a tendency to result in chattering during practical applications. In this work, a novel auxiliary robust integral of the sign of the error (ARISE) controller is proposed to prevent chattering and deal with uncertainties (even those bounded by constants) for general, switched, and nonsmooth control-affine nonlinear systems. The ARISE control system includes a unique auxiliary error that is designed to inject a sliding mode (SM) term directly into the error system without including an SM term in the controller itself. In fact, the ARISE control law includes an integral SM term that is continuous. Consequently, the ARISE control law minimizes the chattering effect that results from discontinuous SM terms. The proposed ARISE control system is augmented with an adaptive update law to deal with the unknown control effectiveness matrix in the dynamic model. To prove the effectiveness of the ARISE controller, a nonlinear stability analysis was conducted and resulted in semi-global exponential tracking towards an ultimate bound. Furthermore, the performance of the proposed controller was evaluated and compared against a traditional SM controller through simulations using a switched Van der Pol oscillator model. It was concluded that the proposed ARISE controller performs better for a switched system than an SM controller. The improved performance of the ARISE controller was consistent across different dynamic parameters and disturbances. ARISE controller; nonlinear control; Lyapunov method +
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding: [EMAIL_ADDRESS]  
Footnote †: Corresponding [EMAIL_ADDRESS]
dynamics can only be upper-bounded by constants. To enhance the performance of the controller and obtain a better stability outcome, robust controllers have been combined with feedforward adaptive terms to compensate for the uncertain parameters [13; 14; 15; 16]. To elaborate, adaptive terms in a control law are capable of reducing the amount of control effort needed for the system to converge since some of the uncertainty has been isolated and approximated by feedforward terms. Thus, a feedforward adaptive term incorporates some dynamic information in the control law, thereby enhancing controller performance. Another approach to compensating for dynamic uncertainties that are bounded by constants is to augment robust or adaptive controllers with discontinuous terms. For example, sliding mode (SM) controllers incorporate a discontinuous signum function within the control law to compensate for these uncertain terms [17; 18; 19; 10]. Theoretically, SM control immensely enhances stability and yields a favorable transient performance; however, the discontinuous signum function within the SM controller architecture introduces abrupt switching within the control input.