scholarly journals Optimal control of spacecraft motion in the vicinity of Eros 433 asteroid

2020 ◽  
Vol 18 (4) ◽  
pp. 146-156
Author(s):  
A. Yu. Shornikov
Keyword(s):  
Optimal Control ◽  
Electric Propulsion ◽  
Control Program ◽  
Low Thrust ◽  
Spacecraft Motion ◽  
Gravitational Fields ◽  
Modified Newton Method ◽  
Time Optimal ◽  
Controlled Motion ◽  
The Pontryagin Maximum Principle

The article describes an algorithm for optimizing controlled motion of a spacecraft equipped with low-thrust electric propulsion engines maneuvering in the vicinity of an object with an irregular gravitational field (asteroid Eros 433). A mathematical model of the object’s gravitational potential and a model of spacecraft motion are presented. The Pontryagin maximum principle is used to get the time-optimal control program. The formulated boundary value problem is solved numerically by the modified Newton method. The described algorithm can be used to solve similar problems of low-thrust flight dynamics in the vicinity of objects with irregular gravitational fields.

scholarly journals Minimum-Fuel Planar Earth-to-Mars Low-Thrust Trajectories Using Bang-Bang Control

2021 ◽  
Author(s):  
Daero Lee
Keyword(s):  
Optimal Control ◽  
Boundary Value Problems ◽  
Electric Propulsion ◽  
Direct Method ◽  
Boundary Value ◽  
Specific Impulse ◽  
Direct Methods ◽  
Optimization Methods ◽  
Low Thrust ◽  
Primer Vector Theory

Recent advance in electric propulsion systems have demonstrated that these engines can be used for for long-duration interplanetary voyages. Constant specific impulse engine described as a thrust-limited engine is an example of this type of engine, processing the ability to operate at a constant level of impulse. The determination of minimum-fuel, planar heliocentric Earth-to-Mars low-thrust trajectories of spacecraft using a constant specific impulse is discussed considering the first-order necessary conditions derived from Lawden’s primer vector theory. The minimum-fuel low-thrust Earth-to-Mars optimization problem is then solved in two-dimensional, heliocentric frame using both indirect and direct methods. In the indirect method, two-point-boundary-value problems are derived to solve boundary value problems for ordinary differential equations. In the direct method, a general-purpose optimal control software called GPOPS-II is adopted to solve these optimal control problems. Numerical examples using two different optimization methods are presented to demonstrate the characteristics of minimum-fuel planar low-thrust trajectories with on-off-on thrust sequences at three chosen flight times and available maximum powers. The results are useful for broad trajectory search in the preliminary phase of mission designs.

Time-Energy Optimal Control of Articulated Systems With Geometric Path Constraints

1996 ◽  
Vol 118 (1) ◽  
pp. 139-143 ◽  
Author(s):  
Zvi Shiller
Keyword(s):  
Optimal Control ◽  
Optimal Trajectory ◽  
Direct Drive ◽  
Initial Value ◽  
Tracking Errors ◽  
Path Constraints ◽  
Dimensional State Space ◽  
Time Optimal ◽  
Articulated Systems ◽  
The Pontryagin Maximum Principle

The motions of articulated systems along specified paths are optimized to minimize a time-energy cost function. The optimization problem is formulated is a reduced two-dimensional state space and solved using the Pontryagin maximum principle. The optimal control is shown to be smooth, as opposed to the typically discontinuous time optimal control. The numerical solution is obtained with a gradient search that iterates over the initial value of one co-state. Optimal trajectories are demonstrated numerically for a two-link planar manipulator and experimentally for the UCLA Direct Drive Arm. The smoother time-energy optimal trajectory is shown to result in smaller tracking errors than the time optimal trajectory.

scholarly journals Quenching Time Optimal Control for Some Ordinary Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Ping Lin
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Parabolic Equations ◽  
Time Optimal Control ◽  
Optimal Controls ◽  
Time Optimal ◽  
Differential Control ◽  
Quenching Time ◽  
The Pontryagin Maximum Principle

This paper concerns time optimal control problems of three different ordinary differential equations inℝ2. Corresponding to certain initial data and controls, the solutions of the systems quench at finite time. The goal to control the systems is to minimize the quenching time. The purpose of this study is to obtain the existence and the Pontryagin maximum principle of optimal controls. The methods used in this paper adapt to more general and complex ordinary differential control systems with quenching property. We also wish that our results could be extended to the same issue for parabolic equations.

Energy savings for ship propulsion in waves based on real-time optimal control of propeller pitch and electric propulsion

2017 ◽  
Vol 22 (3) ◽  
pp. 546-558 ◽  
Author(s):  
Hidenari Makino ◽  
Naoya Umeda ◽  
Toshiyuki Ohtsuka ◽  
Shoji Ikejima ◽  
Hidenori Sekiguchi ◽  
...  
Keyword(s):  
Optimal Control ◽  
Real Time ◽  
Electric Propulsion ◽  
Energy Savings ◽  
Time Optimal Control ◽  
Ship Propulsion ◽  
Time Optimal

scholarly journals Use of the Lyapunov Functions for Calculating the Locally Optimal Control of a Thrust Vector during Low-Thrust Interorbital Transfer

2021 ◽  
Vol 59 (3) ◽  
pp. 212-221
Author(s):  
R. V. Yelnikov
Keyword(s):  
Optimal Control ◽  
Lyapunov Functions ◽  
Electric Propulsion ◽  
Control Algorithm ◽  
Control Technique ◽  
Control Algorithms ◽  
Low Thrust ◽  
The Maximum Principle ◽  
Thrust Vector ◽  
Vector Orientation

Abstract— This paper presents a method for locally optimal control of the thrust vector of the electric propulsion system (EPS) for a spacecraft that performs a multiturn interorbital transfer from the initial elliptical orbit into a geostationary orbit (GSO). The control represents the time dependences of the angles that characterize the EPS thrust vector orientation in space. Here, it is assumed that the EPS is always on. The proposed control algorithm belongs to the class of feedback control algorithms and is based on using the Lyapunov functions. Numerical examples are presented, which characterize the operability of the proposed control technique. Considerable attention is paid to the comparison of given solutions with the optimal solutions obtained within the framework of the maximum principle formalism.

Rendez vous with Saturn's rings

1984 ◽  
Vol 75 ◽  
pp. 743-759 ◽  
Author(s):  
Kerry T. Nock
Keyword(s):  
Solar Energy ◽  
Electric Propulsion ◽  
Power Source ◽  
Propulsion System ◽  
Low Thrust ◽  
Ring Plane ◽  
The Earth ◽  
Total Impulse ◽  
Saturn's Rings

ABSTRACTA mission to rendezvous with the rings of Saturn is studied with regard to science rationale and instrumentation and engineering feasibility and design. Future detailedin situexploration of the rings of Saturn will require spacecraft systems with enormous propulsive capability. NASA is currently studying the critical technologies for just such a system, called Nuclear Electric Propulsion (NEP). Electric propulsion is the only technology which can effectively provide the required total impulse for this demanding mission. Furthermore, the power source must be nuclear because the solar energy reaching Saturn is only 1% of that at the Earth. An important aspect of this mission is the ability of the low thrust propulsion system to continuously boost the spacecraft above the ring plane as it spirals in toward Saturn, thus enabling scientific measurements of ring particles from only a few kilometers.

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