In order to eliminate the inherent harmful chattering phenomenon of sliding mode controller, a high-slope saturation function is used to replace the discontinuous sign function in the sliding mode manifold design.
Apollo, byname Phoebus, in Greek religion, a deity of manifold function and meaning, after Zeus perhaps the most widely revered and influential of all the Greek gods.
Φ is a center manifold function.
To this end, a novel fuzzy integral sliding manifold function is adopted such that the matched uncertainties are completely rejected while the mismatched ones will not be enlarged during the sliding mode phase.
Secondly, to further solve the problem of input saturation, the hyperbolic tangent function and auxiliary system are introduced to design an anti-saturation fast adaptive terminal sliding mode controller which not only can satisfy the requirements of the actuator's physical limitation, but also guarantees that the sliding mode manifold is finite-time stable.
To achieve finite-time performance of sliding mode dynamics, the outer sliding mode surface is designed as a terminal sliding mode manifold, and the inner one is designed as a fast nonsingular terminal sliding mode manifold, respectively.
Since the key point in the proof of Theorem 3.2.1 is the center manifold function, we introduce an approximation formula of the center manifold function derived in [16].
Nor were graphical patterns (e.g., manifold, function or envelope) observed for group data with the standard deviation and median-absolute deviation.
In this paper, a general design scheme is proposed for finite-time switching mode manifolds and corresponding nonsingular controllers.
Glial cells are one source of thrombospondin-1, a matricellular glycoprotein with manifold functions.
