Direct transcription has been employed to transcribe the optimal control problem into a nonlinear programming problem. This paper presents a trajectory optimization method based on a combination of the direct transcription and mesh refinement algorithm. Hermite-Simpson method has the advantage of reasonable accuracy with highly sparse Hessian matrix and constraint Jacobians, and the pseudospectral method provides spectral accuracy for optimal control problems. The optimal control problem is discretized at a series of Legendre-Gauss-Lobatto points, then the trajectory states are approximated by using local Hermite interpolating polynomials. Thus, the method produces significantly smaller mesh size with a higher accuracy tolerance solution. The derived relative error estimation is then used to trade the number of mesh polynomials degree within each mesh interval with the number of mesh intervals. As a result, the suggested method can produce more small mesh size, requires less computation solution for the same optimal control problem. The simulation experiment results show that the suggested method has many advantages.
Based on the theory of fractional order calculus (FOC), a novel extended proportional guidance (EPN) law for intercepting the maneuvering target is proposed. In the first part, considering the memory function and filter characteristic of FOC, the novel extended PN guidance algorithm is developed based on the conventional PN after introducing the properties and operation rules of FOC. Further, with the help of FOC theory, the average load and ballistics characteristics of proposed guidance law are analyzed. Then, using the small offset kinematic model, the robustness of the new guidance law against autopilot parameters is studied theoretically by analyzing the sensitivity of the closed loop guidance system. At last, representative numerical results show that the designed guidance law obtains a better performance than the traditional PN for maneuvering target.
This paper investigates the design of a missile seeker servo system combined with a guidance and control system. Firstly, a complete model containing a missile seeker servo system, missile guidance system, and missile control system (SGCS) was creatively proposed. Secondly, a designed high-order tracking differentiator (HTD) was used to estimate states of systems in real time, which guarantees the feasibility of the designed algorithm. To guarantee tracking precision and robustness, backstepping sliding-mode control was adopted. Aiming at the main problem of projectile motion disturbance, an adaptive radial basis function neural network (RBFNN) was proposed to compensate for disturbance. Adaptive RBFNN especially achieves online adjustment of residual error, which promotes estimation precision and eliminates the “chattering phenomenon”. The boundedness of all signals, including estimation error of high-order tracking differentiator, was especially proved via the Lyapunov stability theory, which is more rigorous. Finally, in considered scenarios, line of sight angle (LOSA)-tracking simulations were carried out to verify the tracking performance, and a Monte Carlo miss-distance simulation is presented to validate the effectiveness of the proposed method.
In this paper, the capturability of retro proportional navigation against high-speed nonmaneuvering targets is analyzed. By using a modified polar coordinate, the equations describing the relative dynamics of the guidance problem become simple. The novel capture region of retro proportional navigation, which is the necessary and sufficient conditions for the interception, is derived by utilizing an auxiliary function. A new constraint condition is added to the derivation of the capture region, which can guarantee capture high-speed targets successfully. Meanwhile, the optimal aiming and the optimal position of interceptor are derived which are used to acquire the excellent initial conditions to capture the high-speed targets. The results show that the capture region of retro proportional navigation is larger compared with pure proportional navigation. Additionally, initial constraint conditions of interceptor in the case of planar engagement are described based on the capture region of retro proportional navigation, which can provide a reference for midcourse trajectory planning. Finally, simulation is performed to verify the feasibility of the initial conditions of the interceptor.
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