Abstract
In this paper, an optimum fuzzy combination of decoupled sliding mode control (DSMC) and adaptive feedback linearization (FBL) is presented for under-actuated nonlinear systems with uncertainties. At first, DSMC and FBL are separately designed and the feedback linearization parameters are adapted by using the gradient descent approach; then, a fuzzy weighted summation of the two controllers is introduced. The multi-objective non-dominated sorting genetic algorithm II (NSGAII) is employed to properly choose the control gains. The objective functions for the optimization process are defined as the integrals of time multiplied by absolute errors, which have been minimized, simultaneously. In addition, the ball and beam system, as a well-known and popular benchmark, is investigated to test and challenge the proposed strategy. Simulation results illustrate that this approach would provide better performance in terms of settling time and control input compared with other methods reported in the literature.
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