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This article first investigates the adaptive fuzzy inverse optimal control design problem for a class of uncertain strict-feedback nonlinear systems. Fuzzy logic systems are utilized to identify the unknown nonlinear dynamics, and then, an equivalent system and an auxiliary system are established. Based on the auxiliary system and using backstepping recursive design algorithm, an adaptive fuzzy inverse optimal scheme, associating with a meaningful objective functional, is developed. It is proved that the presented adaptive fuzzy inverse optimal control scheme can guarantee that the considered system is input-to-state stabilizable and also achieves the goal of inverse optimality with respect to the cost functional. Finally, the simulation studies and comparisons via two examples are provided to confirm the validity of the developed control strategy.
Li et al. (Thu,) studied this question.