Abstract This paper proposes a novel adaptive sliding mode control (ASMC) for a class of polynomial systems comprising uncertain terms and input nonlinearities. In this approach, a new polynomial sliding surface is proposed and designed based on the sum‐of‐squares (SOS) decomposition. In the proposed method, an adaptive control law is derived such that the finite‐time reachability of the state trajectories in the presence of input nonlinearity and uncertainties is guaranteed. To do this, it is assumed that the uncertain terms are bounded and the input nonlinearities belong to sectors with positive slope parameters. However, the bound of the uncertain terms is unknown and adaptation law is proposed to effectively estimate the uncertainty bounds. Furthermore, based on a novel polynomial Lyapunov function, the finite‐time convergence of the sliding surface to a pre‐chosen small neighborhood of the origin is guaranteed. To eliminate the time derivatives of the polynomial terms in the stability analysis conditions, the SOS variables of the Lyapunov matrix are optimally selected. In order to show the merits and the robust performance of the proposed controller, chaotic Chen system is provided. Numerical simulation results demonstrate chattering reduction in the proposed approach and the high accuracy in estimating the unknown parameters.
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