Multi-power combination function reaching law:Basis for sliding mode control algorithm

This paper proposes a novel Multi-power combination function reaching law (MPCFRL) for the problem of slow convergence rate and chattering in systems. Overall gain for the reaching law is designed to be used a new nonlinear function. Merits of incorporating the fast reaching law and the power reaching law, the method presented in this paper ensures the system achieves fast convergence and suppresses the chattering. When there exist external disturbances and model uncertainty, MPCFRL allows sliding mode variables to converge to the steady- state error bound in limited time. And MPCFRL method is to validate the inverted pendulum system, its effectiveness and superiority are verified by simulation results and numerical analysis.