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The location of Low-Altitude Flight Service Station (LAFSS) is a comprehensive decision work, and it is also a multi-objective optimization problem (MOOP) with constraints. As a swarm intelligence search algorithm for solving constrained MOOP, the Immune Algorithm (IA) retains the excellent characteristics of genetic algorithm. Using some characteristic information or knowledge of the problem selectively and purposefully, the degradation phenomenon in the optimization process can be suppressed and the global optimum can be achieved. However, due to the large range involved in the low-altitude transition flight, the geographical characteristics, economic level and service requirements among the candidate stations in the corridor are quite different, and the operational safety and service efficiency are interrelated and conflict with each other. And all objectives cannot be optimal. Therefore, this article proposes a Modified Immune Algorithm (MIA) with two-layer response to solve the constrained multi-objective location mathematical model of LAFSS. The first layer uses the demand track as the cell membrane positioning pattern recognition service response distance to trigger the innate immunity to achieve the basic requirements of security service coverage. In the second layer, the expansion and upgrading of adjacent candidate sites are compared to the pathogen’s effector, and the adaptive immunity is directly or indirectly triggered again through the cloning, mutation and reproduction between candidate sites to realize the multi-objective equilibrium of the scheme. Taking 486,000 km2 of Sichuan Province as an example, MIA for LAFSS is simulated by the MATLAB platform. Based on the Spring open source application framework of Java platform, the cesiumjs map data is called through easyui, and the visualization of site selection scheme is presented with the terrain data of Map World as the background. The experimental results show that, compared with dynamic programming and ordinary immunization, the immune trigger mode of double response and the improved algorithm of operation parameter combination designed by the Taguchi experiment, the total economic cost of location selection is reduced by 26.4%, the service response time is reduced by 25%, the repeat coverage rate is reduced by 29.5% and the effective service area is increased by 17.5%. The security risk, service efficiency and location cost are balanced. The present work is to provide an effective location method for the layout number and location of local transfer flight service stations. For complex scenes with larger scale of low-altitude flight supply and demand and larger terrain changes in the region, the above research methods can be used to effectively split and reduce the dimension.

Reachable set bounding for homogeneous nonlinear systems with delay and disturbance is studied. By the usage of a new method for stability analysis of positive systems, an explicit necessary and sufficient condition is first derived to guarantee that all the states of positive homogeneous time-delay systems with degree p>1 converge asymptotically within a specific ball. Furthermore, the main result is extended to a class of nonlinear time variant systems. A numerical example is given to demonstrate the effectiveness of the obtained results.

We investigate the problem of reachable set bounding for a class of continuous-time and discrete-time nonlinear time-varying systems with time-varying delay. Unlike some preceding works, the involved disturbance input and time-varying delay are not assumed to be bounded. By employing an approach which does not involve the conventional Lyapunov-Krasovskii functional, new conditions are proposed such that all the state trajectories of the system converge asymptotically within a ball. Two illustrative examples are also given to show the effectiveness of the obtained results.