In this study an adaptive critic-based optimal neurocontroller was developed and applied to a non-linear cantilevered plate system to improve its vibrational characteristics. The smart structural system which incorporates a two dimensional aluminum plate mounted with PZT actuators and PVDF sensors is interfaced to a PC with a DAS1600 data acquisition card. The neural network plant model was acquired from a previous study on the setup. Model based design approach was used to design the optimal neuro-controller which minimizes an infinite horizon quadratic cost function by solving the equations obtained by the Dynamic Programming methodology. Two multi-layer perceptron networks the action and the critic were trained off-line for a wide range of initial conditions in the specified range for the state vector. The critic (supervisor) network in our case outputs the co-state vector and critiques the output of the controller network. After convergence to a desired degree of accuracy the action (controller) network gives an optimal output in a feedback form and can be directly incorporated in the control loop. The controller is finally tested for a range of initial conditions and the experimental results were compared for a time response of the plant with and without control.