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论文范文
1. Introduction After decades of development, hypersonic technology has made a lot of progress [1–3]. Hypersonic vehicles will be used in military as precision strike weapons or platforms in the near future. The demand on the research of advanced intercept and defense technology is urgent. In allusion to the high speed and large maneuverability of hypersonic weapons, the interceptor should adopt the compound guidance strategy to improve the success rate of interception. From the end of program control flight to the target acquisition of terminal guidance, the interceptor spends most of the time flying in the midcourse guidance. So the flight performance of midcourse guidance determines the overall performance. If we adopt the traditional guidance method to intercept the high dynamic target directly, it will cause the frequent changes of the trajectory, which is not conducive to the implementation of the interception and leads to unnecessary loss of energy. So it is a reasonable strategy to design the trajectory of midcourse guidance. The main objective of the midcourse guidance is to minimize the energy consumption in the flight process of interceptor and enter the terminal guidance with the best relative geometric relationship [4]. At present, the challenges which the midcourse guidance law design of near space interceptors faces are mainly in the following two aspects: on the one hand, during the flight process of interceptors, problems such as structural strength, thermal protection, normal work of the engine, and control stability give rise to strict requirements on the heat flux, dynamic pressure, overload, control, and other characteristics of the process. Additionally, the predicted impact point (PIP) provides terminal position constraints, and the terminal guidance acquisition state-space becomes the strong constraints conditions of interceptors [5]. On the other hand, in actual flight process, the variation ranges of altitude and velocity are relatively large. Due to the initial conditions errors, atmospheric environment changes, and great uncertainty of aerodynamic model and navigation equipment, it will cause trajectory tracking errors. Furthermore, the nominal trajectory generated before launch is based on remote detection results. In this condition, tracking and prediction of the target have great error. With the approaching of the interceptor and the target, tracking and prediction accuracy will be improved by means of approaching detection with on-board equipment. And the target is also likely to maneuver actively. All those will lead to the change of PIP, and terminal constraints also need updates accordingly. Therefore, the designed midcourse guidance law must have the ability of online trajectory optimization. Taking all kinds of terminal constraints and a series of process characteristics into account, the online optimization problem is actually a complex nonlinear optimization problem [6], and many scholars have studied it. Lin and Tsai [7, 8] obtained a trajectory shaping guidance law by simplifying the model and realized online trajectory generation. But the trajectory was not true optimal due to too much approximation. Indig et al. [6, 9, 10] first linearized the dynamic model of interceptors. According to the location of PIP, the optimal guidance law was designed based on the trajectory shaping guidance. Then, in allusion to the actual nonlinear dynamic model, the terminal angle constraints of interceptor were added according to the midcourse and terminal guidance handover. Finally, the optimal trajectory model was deduced based on Pontryagin minimum principle and solved by Gauss pseudospectral method. Dwivedi et al. [11, 12] studied the problem of midcourse guidance trajectory planning using model predictive static planning method. Based on the state equations of discretized system, the control variables were updated by solving the costate vectors of the whole time period, whose coefficient matrix could be obtained by recursive method. The simulation results show that this method has high accuracy and efficiency. Yakimenko et al. [13–15] proposed a trajectory shaping guidance law based on the inverse dynamic of virtual domain. In this method, the coordinates of aircraft were expressed by higher order polynomials with virtual arc, and the dynamic equations were transformed from the time domain to the virtual domain. Introducing the virtual arc as an argument made it possible to optimize the speed history along the trajectory independently. Additionally, the number of the optimized variables was reduced and the integration process was avoided. By this method, the trajectory can be generated with good convergence robustness. In addition, some scholars have also studied this problem by pseudospectral method [16, 17], intelligent algorithm [18, 19], and so on. 
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