Abstract
This article addresses the problems of the adaptive robust control design and the parameters optimization for a class of underactuated mechanical systems. We describe the uncertainty by using the fuzzy set theory to form the fuzzy dynamical systems. A novel adaptive robust control with two tunable gain parameters is designed based on the formed system, and the nonholonomic servo constraints are also considered in the control design. By employing the principle of the Nash game theory, we establish an optimization method for the two gain parameters, and the Nash equilibrium orients the optimal values of the two gain parameters. Finally, the effectiveness of the designed optimal control is shown by a numerical simulation.
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