When solving combined plant and control optimization (co-design) problems of actual dynamic systems, the models with computationally expensive states derivative functions will often be encountered. Jacobian information cannot be effectively extracted in the optimization process since the expressions of these models are extremely verbose or models are given in the form of simulation programs, which makes gradient-based optimization algorithms difficult. Then the alternative approaches based on finite difference technique are selected. These methods require numerous original expensive evaluations, hence co-design optimizations of these complicated systems are basically not impractical. Here, we propose a new sequential sampling strategy based on error filtering and distance clustering to construct and update surrogate models. The computational cost is significantly reduced through deploying these cheap surrogate models and their easy-to-extract Jacobian information. Dynamic optimization examples of the 2 DOF and 3 DOF robot illustrate the comparison of several sampling strategies and show the feasibility and efficiency of the proposed method. The co-design example of a wind turbine is followed to demonstrate its application prospect in engineering designs.

当解决实际动态系统的工厂和控制优化组合（协同设计）问题时，经常会遇到具有计算量大的状态导数函数的模型。由于这些模型的表达式过于冗长，或者模型以仿真程序的形式给出，因此无法在优化过程中有效地提取Jacobian信息，这使得基于梯度的优化算法变得困难。然后选择了基于有限差分技术的替代方法。这些方法需要大量原始昂贵的评估，因此，对这些复杂系统的共同设计优化基本上是不切实际的。在这里，我们提出了一种新的基于误差过滤和距离聚类的顺序采样策略，以构造和更新代理模型。通过部署这些廉价的代理模型及其易于提取的Jacobian信息，可显着降低计算成本。2自由度和3自由度机器人的动态优化示例说明了几种采样策略的比较，并表明了该方法的可行性和效率。接下来是一个风力涡轮机的共同设计示例，以展示其在工程设计中的应用前景。