Predefined-time fractional-order time-varying sliding mode control and its application in hypersonic vehicle guidance law

In this paper, a predefined-time fractional-order time-varying sliding mode controller is proposed for a class of second-order systems. The state errors are converged to zero at a predefined time, which can be set in advance by an explicit parameter. The stability is proved by Lyapunov second method and the predefined-time convergence is directly proved by solving the analytical formula for the state errors with squeeze theorem and mean value theorem. The sliding mode arrival phase caused by the initial state errors is eliminated in the designed controller, which has stronger robustness. Compared with the integer-order ones, the predefined-time fractional-order time-varying sliding mode controller proposed in this paper has stronger anti-interference ability. The controller is applied to the design of terminal guidance law for hypersonic vehicles. The simulation results show that the designed guidance law can ensure high precision in terms of impact angle error and miss distance under severe interference.