Terminal time regulator-based exact-time sliding mode control for uncertain nonlinear systems

This article proposes a sliding mode control scheme with exact convergence time for uncertain nonlinear systems. Terminal time regulator is defined for designing the global exact-time time-varying sliding mode. The proposed method has the following advantages: first, the reaching phase is absolutely eliminated from the initial time such that the sliding mode invariance is identically guaranteed on an entire dynamics; second, on the sliding mode, the system state converges to the origin exactly at the predefined settling time instant, rather than at an uncertain time instant with boundedness as obtained by existing methods; third, the control signal of the proposed controller is bounded even when the time approaches to the predefined settling time; and fourth, low-pass filtering is utilized to suppress the signal chattering in the discontinuous control while maintaining the system transient behaviors by selecting a proper time constant. Lyapunov analysis verifies that for any initial condition the closed-loop system can terminally converge to zero exactly at the predefined time instant. The proposed control is finally generalized for Euler–Lagrange (EL) systems.