In this paper a new sliding mode control algorithm for the third-order non-linear, time-varying, uncertain system subject to unknown disturbance is proposed. Since the conventional input constraints expressed by inequalities are often impractical, in this paper the situation is considered where the input signal is subject to elastic constraint. It is assumed that the threshold value of the system input signal is known and exceeding this value is undesirable but possible if justified by essential improvement of the system performance. The proposed algorithm employs a time-varying switching plane. At the initial time the plane passes through the point determined by the system initial conditions in the error state space and afterwards moves with a constant velocity to the origin of the space. The plane is designed in such a way that fast error convergence is achieved using limited control input. By this means, the reaching phase is eliminated, insensitivity of the system to external disturbance is ensured from the very beginning of the control action, and fast, monotonic error convergence to zero is achieved. Moreover, it is demonstrated that the conventional input constraint expressed by an inequality is a limit case of the elastic constraint considered in the paper.
Stochastic Modeling and Power Control of Time-Varying Wireless Communication Networks
