The trajectory tracking of under actuated nonlinear system with two degrees of freedom is tackled by an adaptive fuzzy hierarchical\nsliding mode controller. The proposed control law solves the problem of coupling using a hierarchical structure of the sliding\nsurfaces and chattering by adopting different reaching laws.The unknown system functions are approximated by fuzzy logic systems\nand free parameters can be updated online by adaptive laws based on Lyapunov theory. Two comparative studies are made in\nthis paper. The first comparison is between three different expressions of reaching laws to compare their abilities to reduce the\nchattering phenomenon.The second comparison is made between the proposed adaptive fuzzy hierarchical sliding mode controller\nand two other control laws which keep the coupling in the under actuated system. The tracking performances of each control law\nare evaluated. Simulation examples including different amplitudes of external disturbances are made.
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