This paper presents a Three-Dimensional (3D) cooperative guidance law with Practical Predefined-Time (PPT) convergence for multiple missiles considering approach angle (terminal line-of-sight) and simultaneous arrival constraints. To achieve a salvo attack against a maneuvering target from various directions, the guidance problem is tackled by addressing two critical factors: ensuring that the time-of-arrival is consistent and that the desired approach angles can be met. Considering the short duration of the homing guidance process, the convergence with predefined time for guidance states (especially the approach angle and time-to-go) is factored in. First, for the simultaneous arrival, a PPT guidance law is developed, which can meet the same time-to-go convergence rate in the Line-of-Sight (LOS) direction. Then, in the normal LOS direction, a 3D PPT guidance law is presented considering the approach angle constraint so that the desired approach angles can be reached within a user-designed time. The time-based generator technique is employed in the proposed PPT Cooperative Guidance Law (PPTCGL) to avoid the time-varying gain singularity issue. Notably, this technique can allow the convergence time to be preset in advance, independent of initial system conditions and tuning parameters. Additionally, to avoid excessive gain and improve the robustness of guidance law, a PPT disturbance observer is designed against uncertainties and target maneuvers so that the guidance system perturbation can be compensated in real time. It is user-friendly that the convergence of disturbance estimation can be met with a flexible pre-setting time before achieving the terminal guidance constraints. Finally, extensive numerical simulations are conducted to verify the effectiveness and robustness of the proposed PPTCGL in both the nominal cases and the Monte Carlo test.

To address the problem of homing guidance with impact angle constraint or impact time constraint under the condition of limited field-of-view of missile's seeker, a multi-constraint homing guidance law design method based on high-order reshaping of relative range profile is proposed. Firstly, an auxiliary variable containing only field-of-view angle is constructed for the two-dimensional plane homing guidance model, and a high-order polynomial with the reference missile-target relative range profile as the auxiliary variable is designed. Secondly, some profile parameters are solved by using the initial and terminal boundary conditions of guidance, and the expression forms of the parameters to be solved are given by performing terminal constraint integration on the auxiliary variable transformation equation. Furthermore, the impact angle constrained guidance law and impact time constrained guidance law driven by reference profile are given based on model transformation. At the same time, to ensure continuous attenuation of the seeker's field-of-view, the conditions for the profile parameters to be satisfied are given. On this basis, the explicit representation form of the available sets of angle constraint and time constraint are derived. Different from the existing guidance law with profile reshaping, this paper designs a general n-order range profile reshaping guidance method, which can obtain wider achievable constraint sets, and is also convenient for designers/engineers to analyze the reshaping guidance law performance under arbitrary orders. In addition, to solve the profile deviation problem in the ideal profile reshaping process under uncertainty or disturbance, the guidance law is compensated for profile tracking deviation and is robustly corrected, thereby improving the multi-constraint guidance accuracy under complex working conditions. Finally, the effectiveness and robustness of the designed guidance law are verified through numerical simulation comparison analysis under various working conditions and Monte Carlo tests.