约束最优控制理论及其在气动优化中的应用

CONSTRAINED OPTIMUM CONTROL THEORY:APPLICATION TO AERODYNAMIC DESIGN

为了隐式地和自动地处理气动优化中的约束条件,在Jameson的无约束控制论气动优化设计理论基础上发展了有约束的最优控制理论,建立了约束伴随方程方法,并将其成功地应用到了约束气动优化设计中．比较约束伴随方法和Jameson的原始方法,约束优化问题仅仅只需要修改最终伴随方程的物面边界条件和梯度的计算公式而其它项与Jameson原始方法中的完全相同．这表明了基于控制理论的优化方法不仅适用于含有大量设计变量的优化问题,而且也可以很方便地处理约束优化问题．

The constrained optimum aerodynamic design method is developed in the framework of control theory in order to implement all the constraints implicitly and automatically. With the constrained adjoint method developed in this paper, only the boundary condition of adjoint equations and the gradient computation need to be modified slightly as compared with Jameson＇s original unconstrained formula, other terms are maintained the same. It turns out that the control theory based optimization method is very suitable not only for the designs with a large number of design variables but also for the designs with constraints.