Abstract: Aerodynamic character istics of a wing under given flight condit ions are much concerned to designers. Thispaper describes an aerodynamic character istics optimization method of the transonic wing based on the control theoryfor using Euler equations. According to a given cost function, the cor responding adjoint equat ions and boundary conditions described in physical space are der ived. A numer ical method has been developed for solving it, and the sensitivity derivative of the cost function with respect to design variables can be obtained by using a gr id perturbationmethod to calculate t he var iation of the metric matrix, the quasi-Newton algor ithm is used and the procedure of optimizat ion has been built by an effect ive combination of the above several aspects. Some numerical tests have beenmade for the wing dr ag minimization design and the lift coefficient improved as possible. The test results show thedrag coefficient can reduce about twenty percent if the wing shape is optimized. So the present method is effectiveand feasible, and this method may apply to aerodynamic optimization design of much mor e complex configurations,and the computational cost is inexpensive.

Key words: optimization design, control theory, adjoint equation, Euler equation, sensitivity derivative