Arbitrary-Order Continuous Finite-Time Sliding Mode Controller for Fixed-Time Convergence

Obtaining fixed-time convergence has recently gained much attention. In this case, the convergence time does not depend on initial conditions, unlike conventional control schemes. This brief proposes a new algorithm for finite-time sliding mode control, which can provide fixed-time convergence by suitably adding some special non-linear terms in the control design. The proposed control is free from chattering, which is often required in many practical applications. Moreover, it can be generalized to any arbitrary order dynamical system. The convergence of the proposed scheme is proved. The effectiveness of the proposed scheme is verified by comparing with existing methods.