An approach to optimal actuator design based on shape and topology optimisation techniques is presented. For linear diffusion equations, two scenarios are considered. For the first one, best actuators are determined depending on a given initial condition. In the second scenario, optimal actuators are determined based on all initial conditions not exceeding a chosen norm. Shape and topological sensitivities of these cost functionals are determined. A numerical algorithm for optimal actuator design based on the sensitivities and a level-set method is presented. Numerical results support the proposed methodology.

翻译：提出了一种基于形状与拓扑优化技术的最优执行器设计方法。针对线性扩散方程，本文考虑了两种情形：第一种情形下，根据给定初始条件确定最优执行器；第二种情形下，基于所有不超过选定范数的初始条件确定最优执行器。本文推导了相应代价泛函的形状灵敏度与拓扑灵敏度，并据此提出了一种结合水平集方法的数值算法。数值实验结果验证了所提方法的有效性。