Abstract In this paper, a novel strategy using embedding process and sliding surface is proposed. In this method, a state trajectory starting from a given initial point reaches a definite point on a sliding surface in the minimum time, and then tends to the origin along the sliding surface (SS). In the first, a SS is designed, then using an appropriate measure, an embedding is constructed to solve a time optimal control problem such that the system trajectory reaches the SS in minimum time, after that a control is designed such that the system trajectory tends to the origin along the SS. It is well-known that the main disadvantage of the use of sliding mode controls (SMCs) is a phenomenon, the so-called chattering. The proposed SMC here is piecewise continuous and chattering free. Some numerical examples is presented to illustrate the effectiveness and reliability of the proposed method.

Keywords