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

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.