Author

# Zhou Jing

Bio: Zhou Jing is an academic researcher. The author has contributed to research in topics: Soft landing & Optimal control. The author has an hindex of 1, co-authored 1 publications receiving 5 citations.

Topics: Soft landing, Optimal control

##### Papers

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01 Jan 2007

TL;DR: In this paper, a three dimensional dynamics for the soft landing of a lunar lander is presented, and an optimal control law based on the maximum principle is proposed to realize the minimal fuel strategy.

Abstract: Precise three dimensional dynamics for lunar soft landing were presented.To realize the minimal fuel strategy,an optimal control law was proposed based on the maximum principle.By solving the two-point boundary value problem with concern of both velocity and position restrictions,the optimal trajectory of lunar soft landing was obtained.Simulation results show that the performance of the proposed precise model excels that of the model without consideration of the moon rotation.

5 citations

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TL;DR: In this paper, the authors considered an optimal control problem arising from the optimal guidance of a lunar module to achieving soft landing, where the description of the system dynamics is in a three-dimensional coordinate system.

Abstract: In this paper, we consider an optimal control problem arising from the optimal guidance of a lunar module to achieving soft landing, where the description of the system dynamics is in a three-dimensional coordinate system. Our aim is to construct an optimal guidance law to realize the soft landing of the lunar module with the terminal attitude of the module to be within a small deviation from being vertical with respect to lunar surface, such that the fuel consumption and the terminal time are minimized. The optimal control problem is solved by applying the control parameterization technique and a time scaling transform. In this way, the optimal guidance law and the corresponding optimal descent trajectory are obtained. We then move on to consider an optimal trajectory tracking problem, where a desired trajectory is tracked such that the fuel consumption and the minimum time are minimized. This optimal tracking problem is solved using the same approach to the first optimal control problem. Numerical simulations demonstrate that the approach proposed is highly efficient.

17 citations

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TL;DR: This paper presents a practical method to calculate an approximate optimal feedback gain matrix, without having to solve an optimal control problem involving the complex Riccati-like matrix differential equation coupled with the original system dynamics.

Abstract: In this paper, the task of achieving the soft landing of a lunar module such that the fuel consumption and the flight time are minimized is formulated as an optimal control problem. The motion of the lunar module is described in a three dimensional coordinate system. We obtain the form of the optimal closed loop control law, where a feedback gain matrix is involved. It is then shown that this feedback gain matrix satisfies a Riccati-like matrix differential equation. The optimal control problem is first solved as an open loop optimal control problem by using a time scaling transform and the control parameterization method. Then, by virtue of the relationship between the optimal open loop control and the optimal closed loop control along the optimal trajectory, we present a practical method to calculate an approximate optimal feedback gain matrix, without having to solve an optimal control problem involving the complex Riccati-like matrix differential equation coupled with the original system dynamics. Simulation results show that the proposed approach is highly effective.

10 citations

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01 Jan 2011

TL;DR: In this article, the authors derived a three dimensional dynamics to describe the motion of the module for the powered descent part by introducing three coordinate frames with consideration of the moon rotation, and then, they move on to construct an optimal guidance law to achieve the lunar module soft landing which is treated as a continuously powered descent process with a constraint on the angle between its longitudinal axis and the moon surface.

Abstract: In this thesis, we deal with several optimal guidance and control problems of the spacecrafts arising from the study of lunar exploration. The research is composed of three parts: 1. Optimal guidance for the lunar module soft landing, 2. Spacecraft attitude control system design basing on double gimbal control moment gyroscopes (DGCMGs), and 3. Synchronization motion control for a class of nonlinear system.To achieve a precise pinpoint lunar module soft landing, we first derive a three dimensional dynamics to describe the motion of the module for the powered descent part by introducing three coordinate frames with consideration of the moon rotation. Then, we move on to construct an optimal guidance law to achieve the lunar module soft landing which is treated as a continuously powered descent process with a constraint on the angle of the module between its longitudinal axis and the moon surface. When the module reaches the landing target, the terminal attitude of the module should be within an allowable small deviation from being vertical with reference to lunar surface. The fuel consumption and the terminal time should also be minimized. The optimal descent trajectory of the lunar module is calculated by using the control parameterization technique in conjunction with a time scaling transform. By these two methods, the optimal control problem is approximated by a sequence of optimal parameter selection problems which can be solved by existing gradient-based optimization methods. MISER 3.3, a general purpose optimal control software package, was developed based on these methods. We make use of this optimal control software package to solve our problem. The optimal trajectory tracking problem, where a desired trajectory is to be tracked with the least fuel consumption in the minimum time, is also considered and solved.With the consideration of some unpredicted situations, such as initial point perturbations, we move on to construct a nonlinear optimal feedback control law for the powered deceleration phase of the lunar module soft landing. The motion of the lunar module is described in the three dimensional coordinate system. Based on the nonlinear dynamics of the module, we obtain the form of an optimal closed loop control law, where a feedback gain matrix is involved. It is then shown that this feedback gain matrix satisfies a Riccati-like matrix differential equation. The optimal control problem is first solved as an open loop optimal control problem by using the time scaling transform and the control parameterization method. By virtue of the relationship between the optimal open loop control and the optimal closed loop control along the optimal trajectory, we present a practical method to calculate an approximate optimal feedback gain matrix, without having to solve an optimal control problem involving the complex Riccati-like matrix differential equation coupled with the original system dynamics.To realize the spacecraft large angle attitude maneuvers, we derive an exact general mathematical description of…

3 citations

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25 Sep 2009TL;DR: In this article, a closed loop optimal control law is designed with a parameter matrix K to be determined which is the solution of a riccati-like differential equation, such that it is avoided to solve the complex Riccati like differential equation.

Abstract: In this paper, the optimal control problem to achieve lunar module soft landing with least fuel consumption is considered. The precise three dimensional dynamics is employed to describe the motion of the lunar module. By introducing two new state equations, a closed loop optimal control law is designed with a parameter matrix K to be determined which is the solution of a riccati like differential equation. We present a practical method to calculate the matrix K, such that it is avoided to solve the complex riccati like differential equation. Simulation results show the efficiency of the proposed method.

3 citations

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26 Aug 2014

TL;DR: An asteroid landing trajectory optimization method is studied based on Gauss Pseudo-spectral Method, which is used to disperse the optimal control problem into a nonlinear programming problem and solves the non linear programming problem.

Abstract: An asteroid landing trajectory optimization method is studied based on Gauss Pseudo-spectral. Firstly, we analyze the characteristics of probe landing on asteroid, and put forward the initial conditions, process constraints, terminal constraints and the optimization performance index. The probe's landing trajectory optimization should meet the index. Secondly, Gauss Pseudo-spectral Method is used to disperse the optimal control problem into a nonlinear programming problem. Finally, SQP algorithm solves the nonlinear programming problem. We present the landing trajectory from the hover point to just a fix-point with leveled thrust. Simulation results show that the methodology proposed in this paper has good robustness and convergence.

3 citations