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An adaptive dynamic output feedback neural network controller for a class of multi-input/multi-output affine in the control uncertain nonlinear systems is designed, capable of guaranteeing prescribed performance bounds on the system's output as well as boundedness of all other closed loop signals. It is proved that simply guaranteeing a boundedness property for the states of a specifically defined augmented closed loop system is necessary and sufficient to solve the problem under consideration. The proposed dynamic controller is of switching type. However, its continuity is guaranteed, thus alleviating any issues related to the existence and uniqueness of solutions. Simulations on a planar two-link articulated manipulator illustrate the approach.