A smart functionally graded plate consists of a plate made of a functionally gradient material and actuators made of an active material. The active material, a layer or set of patches, is bonded on the metal-rich surface of the functionally graded plate. When the ceramic-rich surface of the substrate is subjected to thermomechanical loadings, displacements, and stresses may be controlled, and vibration amplitudes may be suppressed by the actuators with supplied electric power. In the attempt towards a basic understanding of the new type of smart structural system, this study considers a benchmark problem, namely, the bending of a functionally graded rectangular plate with an attached piezoelectric actuator. The transfer matrix and asymptotic expansion techniques are employed to obtain a three-dimensional asymptotic solution. In numerical computations, the locally effective material properties of the functionally gradient material are estimated by the Mori-Tanaka scheme. The three-dimensional distributions of displacements and stresses for different volume fractions of the ceramic and metallic constituents could serve as benchmark results to assess approximate theories and numerical methods.