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This paper develops a finite-time dynamic surface control (DSC) scheme for nonlinear systems with mismatched uncertainties via a high-order sliding mode(HOSM) observer. By designing a second-order terminal sliding surface based on the estimated signals, an observer-based sliding mode control (SMC) is designed to counteract the mismatched uncertainties in each step of backstepping. The proposed DSC scheme exhibits the following two attractive features. One is the application of HOSM observer to deal with mismatched system uncertainty functions. This is very different from the traditional approximator-based adaptive methods in dealing with high-order uncertain nonlinear systems. The other is the finite-time convergence of the provided algorithm, which guarantees the transient performance of tracking signals. Especially, the finite convergence time is explicitly given in the controller design and stability analysis. Simulation results of numerical example illustrates that the proposed approach shows better control performance than traditional approximators-based adaptive methods.

Finite-time dynamic surface approach to nonlinear systems with mismatched uncertainties