The leader–follower structure is widely used in unmanned aerial vehicle formation. This paper adopts the proportional-integral-derivative (PID) and the linear quadratic regulator controllers to construct the leader–follower formation. Tuning the PID controllers is generally empirical; hence, various surrogate models have been introduced to identify more refined parameters with relatively lower cost. However, the construction of surrogate models faces the problem that the singular points may affect the accuracy, such that the global surrogate models may be invalid. Thus, to tune controllers quickly and accurately, the regional surrogate model technique (RSMT), based on analyzing the regional information entropy, is proposed. The proposed RSMT cooperates only with the successful samples to mitigate the effect of singular points along with a classifier screening failed samples. Implementing the RSMT with various kinds of surrogate models, this study evaluates the Pareto fronts of the original simulation model and the RSMT to compare their effectiveness. The results show that the RSMT can accurately reconstruct the simulation model. Compared with the global surrogate models, the RSMT reduces the run time of tuning PID controllers by one order of magnitude, and it improves the accuracy of surrogate models by dozens of orders of magnitude.

Bayesian Optimization is a widely applied efficient framework for updating the surrogate model sequentially. To improve the efficiency, multi-fidelity Bayesian Optimization is developed to combine the information of samples in different fidelity levels. However, the multi-fidelity levels brings the challenge for sequential sampling. In multi-fidelity Bayesian Optimization, the sampling strategy is applied to determine not only the sample location but also the sample fidelity level for updating the model. To balance the benefit and the experiment cost, it is vital to measure the potential effect of each fidelity sample. Some sampling strategies, which is categorized as direct-type methods, can measure the potential effect of different samples in a easy way, but they cannot figure out the difference of samples that has little uncertainty and it has the risk for redundant sampling. Some other strategies, which is categorized as direct-type methods, can measure the potential effect appropriately, but the calculation of them are much complicated and time-consuming. In this paper, a new type method combining the direct-type and indirect-type methods is presented for measuring the potential effect of different fidelity sample. It is convenient enough and can avoid the problems occurring in the direct-type method. Based on this paradigm, a sampling strategy named decreased max-value entropy search(DMES) is proposed and applied in the multi-fidelity Bayesian Optimization framework. The characteristics of DMES and how it is different from direct-type method are detailed in some examples. Besides, two numerical experiments and one simulation experiment demonstrate the efficiency of DMES.

No abstract

Because the collapse of complex systems can have severe consequences, vulnerability is often seen as the core problem of complex systems. Multilayer networks are powerful tools to analyze complex systems, but complex networks may not be the best choice to mimic subsystems. In this work, a cellular graph (CG) model is proposed within the framework of multilayer networks to analyze the vulnerability of complex systems. Specifically, cellular automata are considered the vertices of a dynamic graph-based model at the microlevel, and their links are modeled by graph edges governed by a stochastic model at the macrolevel. A Markov chain is introduced to illustrate the evolution of the graph-based model and to obtain the details of the vulnerability evolution with low-cost inferences. This CG model is proven to describe complex systems precisely. The CG model is implemented with two actual organizational systems, which are used on behalf of the typical flat structure and the typical pyramid structure, respectively. The computational results show that the pyramid structure is initially more robust, while the flat structure eventually outperforms it when being exposed to multiple-rounds strike. Finally, the sensitivity analysis results verify and strengthen the reliability of the conclusions.