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In this paper, optimal guidance law design considering fixed final state and time for the final phase booster landing problem of a spacecraft or launch vehicle is investigated and studied. This guidance law, not only satisfied a specific optimality criterion, but it also has the least sensitivity to the initial state’s deviations; which is due to the inclusion of the nonlinear terms in the mathematical modeling using the high order expansions method. The main goal of this research, is to investigate the development and to augment the capability of the high order expansions method for guidance law design. Different implementations of this approach including the differential algebra high order, the generating function based high order and vectorized high order expansions methods have been investigated. After reviewing the implementation concepts of the high order expansions method, the effectiveness of this method has been studied. Then a 3-dimensional booster landing problem has been chosen as the case study and after extracting the mathematical model and nominal optimal solution, the sensitivity variables have been extracted up to the 3rd order. Afterwards, to investigate the performance of the designed guidance law, the Monte Carlo simulations have been performed and it has been shown that the designed guidance law on the basis of the Taylor series and high order expansions method has a good accuracy and is a valuable alterative to the nominal trajectory tracking guidance approach.

The proper angle of launching air defense balls is very important in the probability of the projectile hitting the air target. If the projectile hits the air target, defense costs are saved and damage is not allowed by the enemy. In other words, the ability to hit the target is mainly The reason for cost reduction is essential for modern air cannon systems. The purpose of determining the pre-aiming angles of a projectile is the initial orientation of a bullet firing system in order to hit the intended target, which is addressed in fire control issues, in such a way that the required information is given to the fire control system, and the system after analysis The information selects the most suitable angle and fires the projectile at the target. In this research, we are looking for a solution to determine the pre-target angles of a projectile to hit an aerial target, or in other words, to control the fire to hit an air defense ball on the target. In order to prevent further damage by the enemy while reducing defense costs. In this regard, the problem is first examined in two-dimensional mode, then the problem is considered in three dimensions, in order to calculate the most suitable angle in the fastest time, MLP neural network will be used in this research.

In this research the main goal is to compare the performance of Vectorized High Order Expansions and SDRE method for vertical landing of booster. To this end, at first a comprehensive study of references related to both Vectorized High Order and SDRE method has been performed. Then, the Vectorized High Order Expansions method and the implementation in optimal control problems has been introduced. After that, the SDRE method has been reviewed briefly, and the landing problem has been solved using both methods. To evaluate the performance, a set of various simulations have been performed for both methods and with respect to different initial deviations. By means of simulation results, the performance of both method is studied with regard to landing point errors. To achieve this, statistical results of terminal state errors have been calculated for both method with respect to different initial deviation to evaluate and compare both method, quality-wise.

In this study, terminal phase guidance of a vertical-landing booster has been considered. At first, dynamical equations have been derived assuming variable mass, density and gravity model. Then by considering these parameters as constants, sensitivity variables have been extracted using the vectorized high order expansions method. By using these sensitivity variables, a guidance law for updating optimal path and commands has been given. By implementing this guidance law, and considering initial deviations, near optimal path and guidance command have been extracted online, and the performance has been studied by means of simulations. To this end, intrinsic errors of the theory has been considered and confirmed at first. Then, a set of simulations considering variable mass, density and gravity have been implemented and the performance of the method has been evaluated in the presence of a vast variety of initial deviations. By investigating the results, which have been presented as graphs and numerical errors it can be seen that the landing errors are small and for booster landing mission, the vectorized high order method shows remarkable performance.

In recent years, according to progress of aerospace industries particularly satellites it has been paying much attention to attitude determination of satellite. Attitude determination of satellite in various ways, such as: radio, radar, optical methods and using GPS, q and kalman filter is done, that each of these methods has advantages and disadvantages. Due to disturbance in space, high accuracy in attitude determination, various algorithms to obtain properly accurately attitude, desirable access to position, velocity and time of satellite to achieve desired attitude determination satellite are considered a top priority. However in this Paper, first we review the various methods for attitude determination satellite and then examine of operation and relations of algorithms discussed. This Paper focus on the advantages and disadvantages of qEKF algorithm in compare to other methods are available.