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The purpose of this paper is to propose a hybrid optimization approach with high level of solving precision and efficiency for endo-atmospheric ascent trajectory planning of launch vehicles.

Based on the indirect method of optimal control problems, the optimal endo-atmospheric ascent problem with path constraints and final condition constraints is transformed into a Hamiltonian two point boundary value problem (TPBVP). An advanced Gauss pseudo-spectral method is applied to change the Hamiltonian TPBVP into a system of nonlinear algebraic equations, which is solved by a modified Newton method. To guarantee the convergence of the solution, analytical initial guess technology and homotopy technology are also introduced. At last, simulation tests are made.

The hybrid approach for optimal endo-atmospheric ascent trajectory planning has both fast convergence rate and high solution precision. The simulation results indicate that not only the proposed method is feasible but also it is better than the indirect method, which is a most popular approach for solving the optimal endo-atmospheric ascent problem. Given the same degree of solution accuracy, the new method consumes quite less time on the CPU than that of the indirect method.

The new optimization approach has high level of both solution accuracy and efficiency. It can be used in rapid trajectory designing, on-line trajectory planning and closed-loop guidance of launch vehicles. Also, the proposed Gauss pseudo-spectral method in this paper is a new and efficient method for solving general TPBVPs.

The paper provides a new hybrid optimization method for rapid endo-atmospheric ascent trajectory planning of launch vehicles.

This paper aims to investigate the problem of on-line orbit planning and guidance for an advanced upper stage.

The double impulse optimal transfer orbit is planned by the Lambert algorithm and the improved particle swarm optimization (IPSO) method, which can reduce the total velocity increment of the transfer orbit. More specially, a simplified formula is developed to obtain the working time of the main engine for two phases of flight based on the theorem of impulse. Subsequently, the true anomalies of the start position and the end position for both two phases are planned by the Newton iterative algorithm and the Kepler equation. Finally, the first phase of flight is guided by a novel iterative guidance (NIG) law based on the true anomaly update with respect to the geometrical relationship. Also, a completely analytical powered explicit guidance (APEG) law is presented to realize orbital injection for the second phase of flight.

Simulations including Monte Carlo and three typical orbit transfer missions are carried out to demonstrate the efficiency of the proposed scheme.

A novel on-line orbit planning algorithm is developed based on the Lambert problem, IPSO optimization method and Newton iterative algorithm. The NIG and APEG are presented to realize the designed transfer orbit for the first and second phases of flight. Both two guidance laws achieve higher orbit injection accuracies than traditional guidance laws.

This paper aims to develop a novel trajectory optimization algorithm which is capable of producing high accuracy optimal solution with superior computational efficiency for the hypersonic entry problem.

A two-stage trajectory optimization framework is constructed by combining a convex-optimization-based algorithm and the pseudospectral-nonlinear programming (NLP) method. With a warm-start strategy, the initial-guess-sensitive issue of the general NLP method is significantly alleviated, and an accurate optimal solution can be obtained rapidly. Specifically, a successive convexification algorithm is developed, and it serves as an initial trajectory generator in the first stage. This algorithm is initial-guess-insensitive and efficient. However, approximation error would be brought by the convexification procedure as the hypersonic entry problem is highly nonlinear. Then, the classic pseudospectral-NLP solver is adopted in the second stage to obtain an accurate solution. Provided with high-quality initial guesses, the NLP solver would converge efficiently.

Numerical experiments show that the overall computation time of the two-stage algorithm is much less than that of the single pseudospectral-NLP algorithm; meanwhile, the solution accuracy is satisfactory.

Due to its high computational efficiency and solution accuracy, the algorithm developed in this paper provides an option for rapid trajectory designing, and it has the potential to evolve into an online algorithm.

The paper provides a novel strategy for rapid hypersonic entry trajectory optimization applications.

The purpose of this paper is to analyze the frame of a missile formation cooperative control system, and present an optimal keeping controller of a missile formation in the cooperative engagement.

A missile relative motion model is established directly based on the kinematics relationships in the relative coordinated frame, following that is the detailed process of designing an optimal formation controller, which is analyzed through the small disturbance linearized method and transforming control variables method, respectively, these two methods both have themselves properties. The equations and control variables are intuitive during the linearized analysis, but errors brought by the linearized method are unavoidable, which will reduce the control precision. As for the transforming method, the control accuracy is greatly increased although the control form is a little complex, so in this paper the transforming control variable method is mainly researched to design an optimal formation controller. Considering the states of a leader as input perturbation variables, we design an optimal formation controller based on the linear quadric theory, which has quadric optimal performances of the missile flight states and control quantity. In order to obtain a higher accurate solution, the precise integration algorithm is introduced to solve the Riccati Equation that significantly affects the accuracy of an optimal control problem.

The relative motion model established directly in the relative coordinate frame has intuitive physical significance, and the optimal controller based on this relative motion model is capable of restraining the invariable or slowly varying perturbation brought by the velocity of a leader and the input perturbations caused by the maneuver of the leader, at the same time this optimal controller can implement formation reconfiguration and keeping to an expected states rapidly, steadily and exactly; the steady errors can be greatly decreased by analyzing the relative motion model through transforming control variables method compared to the small disturbance linearized operation.

The main frame of a missile formation cooperative engagement system can be found in this paper, which shows a clear structure and relations of each part of this complex system. The relations between each subsystem including the specific input and output variables can also be used to guide and restrict how to design each subsystem. The emphasis of this paper is on designing an optimal formation keeping controller which can overcome slowly varying or invariable perturbations and implement quadric optimal keeping control rapidly, stably and accurately.

This paper provides a new method to analyze the missile relative motion model. The proposed proportional and integral (PI) optimal controller based on this model, and utilizing the Precise Integration Algorithm to solve this optimal controller are also new thoughts for formation control problems.