Application of adaptive sliding mode control for nonlinear systems with unknown polynomial bounded uncertainties

Abstract

In this paper, we discuss the application of a novel switching integral-exponential-adaptation-law-based adaptive sliding mode control design for a wide class of nonlinear systems with unknown polynomial bounds on the uncertainty norm. A robust finite time convergence, i.e. finite stability, is obtained with low chatter on control actions and a fast-transient performance for adaptive sliding mode control handling the multi-input multi-output nonlinear systems with uncertainties of amplitudes bounded within unknown polynomials in the state vector norm. The exponential term of the proposed adaptation law targets the reduction of the chatter levels of the sliding mode by significantly reducing the gain overestimation while simultaneously suppressing the overshoot by speeding up the system response to the uncertainties. It also prevents the instability issues which encounters the classic integral-gain-law-based adaptive sliding mode control when underestimating its initial gain or gain rate parameter. A simple example illustrates the motivation and feasibility of the proposed adaptive sliding mode control. The applications on a nonlinear mass–spring system and on a two degree of freedom electromechanical rotative plant demonstrate the effectiveness of the proposed design.

Leader-follower formation tracking for differential-drive wheeled mobile robots with uncertainties and disturbances based on immune fuzzy quasi-sliding mode control

“…This type of AIS scheme is widely applied in PID-type controllers gain adjustment as in [28] for a WMR control (but without considering disturbances effects), and [29][30][31][32][33][34][35][36][37], for other control systems, to mention a few. In SMC, since the uncertainties are usually unknown, difficult to model accurately and rarely estimated a priori, considering a conservative control law with a large switching gain is often necessary to guarantee the system stability and a fast tracking convergence, but it can cause an undesired great amount of high-magnitude chattering, actuator saturation and unnecessary energy loss [13,[38][39][40]. For this reason, an AIS inspired by the humoral immune response mechanism is proposed to perform an adaptive adjustment of the magnitude of the control effort by replacing the constant gain of the switching portion of a conventional SMC.…”