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International Conference on Engineering Technology and Application (ICETA)

作者： Wei, Changzhu Huang, Rong Li, Hao Shan, Yongzhi Harbin Inst Technol Dept Aerosp Engn Sch Astronaut Harbin 150006 Heilongjiang Peoples R China Harbin Jiancheng Grp Co Ltd Harbin Heilongjiang Peoples R China

The trajectory optimization technology is one of the key technologies for hypersonic air-vehicle. There are multiple constraints in the process of hypersonic flight, such as uncertainty of flight environment, thermal current, dynamic pressure and overload. The trajectory optimization of hypersonic air-vehicle is facing with a great challenge. This article studies the direct shooting method, the Gauss pseudo spectral method and sequential gradient-restoration algorithm, among which the direct shooting method simply makes the control variables discrete in the time domain, and obtains the status value by explicit numerical integration;Gauss pseudo spectral method makes the status variable and control variable discrete in a series of Gauss points, and constructs multinomial to approximate to the status and control variable by taking the discrete points as the nodes;sequential gradient-restoration algorithm uses iteration to meet the constraints and minimize the increment of initial value of control and status variable in order to constantly approximate to the optimal solution on condition that the constraints meet first order approximation. Finally this article conducts a numerical simulation by taking the diving segment of hypersonic air-vehicle as an example for comparative analysis on those three algorithms respectively from, such as, the initial value selection, constraint handling, convergence speed and calculation accuracy. The simulation result indicates Gauss pseudo spectral method is a method with fairly good comprehensive performance.

关键词： hypersonic air-vehicle direct shooting method Gauss pseudo spectral method sequential gradient-restoration algorithm

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Optimization and Analysis on Trajectory with Multiple Constraints for Hypersonic Air-vehicle

Optimization and Analysis on Trajectory with Multiple Constr...

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The 2015 2nd International Conference on Engineering Technology and Application

作者： Changzhu Wei Rong Huang Hao Li Yongzhi Shan Department of Aerospace Engineering School of AstronauticsHarbin Institute of Technology Harbin Jiancheng Group Co.Ltd

The trajectory optimization technology is one of the key technologies for hypersonic *** are multiple constraints in the process of hypersonic flight,such as uncertainty of flight environment,thermal current,dynamic pressure and *** trajectory optimization of hypersonic air-vehicle is facing with a great *** article studies the direct shooting method,the Gauss pseudo spectral method and sequential gradient-restoration algorithm,among which the direct shooting method simply makes the control variables discrete in the time domain,and obtains the status value by explicit numerical integration;Gauss pseudo spectral method makes the status variable and control variable discrete in a series of Gauss points,and constructs multinomial to approximate to the status and control variable by taking the discrete points as the nodes;sequential gradient-restoration algorithm uses iteration to meet the constraints and minimize the increment of initial value of control and status variable in order to constantly approximate to the optimal solution on condition that the constraints meet first order *** this article conducts a numerical simulation by taking the diving segment of hypersonic air-vehicle as an example for comparative analysis on those three algorithms respectively from,such as,the initial value selection,constraint handling,convergence speed and calculation *** simulation result indicates Gauss pseudo spectral method is a method with fairly good comprehensive performance.

关键词： hypersonic air-vehicle direct shooting method Gauss pseudo spectral method sequential gradient-restoration algorithm

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Optimal starting conditions for the rendezvous maneuver, Part 2:: Mathematical programming approach

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2008年第3期137卷 625-639页

作者： Miele, A. Ciarcia, M. Rice Univ Aeroastronaut Grp Houston TX 77251 USA

In a companion paper (Part 1, J. Optim. Theory Appl. 137(3), 2008), we determined the optimal starting conditions for the rendezvous maneuver using an optimal control approach. In this paper, we study the same problem with a mathematical programming approach. Specifically, we consider the relative motion between a target spacecraft in a circular orbit and a chaser spacecraft moving in its proximity as described by the Clohessy-Wiltshire equations. We consider the class of multiple-subarc trajectories characterized by constant thrust controls in each subarc. Under these conditions, the Clohessy-Wiltshire equations can be integrated in closed form and in turn this leads to optimization processes of the mathematical programming type. Within the above framework, we study the rendezvous problem under the assumption that the initial separation coordinates and initial separation velocities are free except for the requirement that the initial chaser-to-target distance is given. In particular, we consider the rendezvous between the Space Shuttle (chaser) and the International Space Station (target). Once a given initial distance SS-to-ISS is preselected, the present work supplies not only the best initial conditions for the rendezvous trajectory, but simultaneously the corresponding final conditions for the ascent trajectory.

关键词： space trajectories rendezvous optimization guidance transformation techniques mathematical programming sequential gradient-restoration algorithm

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Optimal trajectories for spacecraft rendezvous

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2007年第3期132卷 353-376页

作者： Miele, A. Weeks, M. W. Ciarcia, M. Rice Univ Aeroastronaut Grp Houston TX 77251 USA NASA Lyndon B Johnson Space Ctr Aerosci & Flight Mech Div Houston TX 77058 USA

The efficient execution of a rendezvous maneuver is an essential component of various types of space missions. This work describes the formulation and numerical investigation of the thrust function required to minimize the time or fuel required for the terminal phase of the rendezvous of two spacecraft. The particular rendezvous studied concerns a target spacecraft in a circular orbit and a chaser spacecraft with an initial separation distance and separation velocity in all three dimensions. First, the time-optimal rendezvous is investigated followed by the fuel-optimal rendezvous for three values of the max-thrust acceleration via the sequential gradient-restoration algorithm. Then, the time-optimal rendezvous for given fuel and the fuel-optimal rendezvous for given time are investigated. There are three controls, one determining the thrust magnitude and two determining the thrust direction in space. The time-optimal case results in a two-subarc solution: a max- thrust accelerating subarc followed by a max-thrust braking subarc. The fuel-optimal case results in a four-subarc solution: an initial coasting subarc, followed by a max- thrust braking subarc, followed by another coasting subarc, followed by another max-thrust braking subarc. The time-optimal case with fuel given and the fuel-optimal case with time given result in two, three, or four-subarc solutions depending on the performance index and the constraints. Regardless of the number of subarcs, the optimal thrust distribution requires the thrust magnitude to be at either the maximum value or zero. The coasting periods are finite in duration and their length increases as the time to rendezvous increases and/or as the max allowable thrust increases. Another finding is that, for the fuel-optimal rendezvous with the time unconstrained, the minimum fuel required is nearly constant and independent of the max available thrust. Yet another finding is that, depending on the performance index, constraints, and initial

关键词： space trajectories rendezvous optimal control calculus of variations Mayer problems Bolza problems transformation techniques sequential gradient-restoration algorithm

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Optimal dive recovery maneuvers of a supermaneuvering jet fighter aircraft

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JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS 2001年第2-3期338卷 113-132页

作者： Miele, A Dabney, JB Rice Univ AeroAstronaut Grp Houston TX 77251 USA Univ Houston Dept Syst Engn Clear Lake TX USA

This paper describes an investigation of dive recovery maneuvers of a jet fighter aircraft capable of flying at angles of attack in the post-stall region. In a dive recovery maneuver, the pilot attempts to return the aircraft to level flight at an airspeed such that level flight can be maintained afterward. This maneuver is needed after either an intentional dive or an unintentional dive, or as the terminal recovery stage from some unusual attitude, namely, combination of extremely low airspeed and very high flight path angle. The optimization criterion is the minimization of the maximum loss of altitude during the dive recovery;hence, the optimization problem is a minimax problem of optimal control. The flight dynamics model accounts for all of the factors necessary to accurately characterize the aircraft motion. The results show that the optimal dive recovery trajectories consist of one to three segments, depending on the initial speed and flight path angle. For relatively high initial speed, the optimal trajectory consists of a single segment: a pitch-up at the limiting load factor. For very low initial speed, the optimal trajectory consists of two segments: a supermaneuver flown at very large angles of attack, followed by a pitch-up at the limiting load factor. For unusual attitude recovery from the combination of very low initial speed and very high initial flight path angle, the optimal trajectory consists of three segments: a dive initiation segment, followed by a supermaneuver at very large angles of attack, followed by a pitch-up at the limiting load factor, For aircraft without supermaneuver capability, the supermaneuver segment is to be replaced by a maximum angle of attack segment. The paper concludes with a discussion of the design benefits accrued via supermaneuver capability as well as the operational benefits accrued via afterburner usage. (C) 2001 The Franklin Institute. Published by Elsevier Science Ltd. All rights reserved.

关键词： optimal trajectories dive recovery maneuvers unusual attitude recovery maneuvers supermaneuvers jet fighter aircraft sequential gradient-restoration algorithm

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Optimal control of a ship for course change and sidestep maneuvers

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1999年第2期103卷 259-282页

作者： Miele, A Wang, T Chao, CS Dabney, JB Rice Univ Aero Astronaut Grp Houston TX 77251 USA Rice Univ Dept Mech Engn Houston TX 77251 USA

We consider a ship subject to kinematic, dynamic, and moment equations and steered via rudder under the assumptions that the rudder angle and rudder angle time rate are subject to upper and lower bounds. We formulate and solve four Mayer problems of optimal control, the optimization criterion being the minimum time. Problems P1 and P2 deal with course change maneuvers. In Problem P1, a ship initially in quasi-steady state must reach the final point with a given yaw angle and zero yaw angle time rate. Problem P2 differs from Problem P1 in that the additional requirement of quasi-steady state is imposed at the final point. Problems P3 and P4 deal with sidestep maneuvers. In Problem P3, a ship initially in quasi-steady state must reach the final point with a given lateral distance, zero yaw angle, and zero yaw angle time rate. Problem P4 differs from Problem P3 in that the additional requirement of quasi-steady state is imposed at the final point. The above Mayer problems are solved via the sequential gradient- restoration algorithm in conjunction with a new singularity avoiding transformation which accounts automatically for the bounds on rudder angle and rudder angle time rate. The optimal control histories involve multiple subarcs along which either the rudder angle is kept at one of the extreme positions or the rudder angle time rate is held at one of the extreme values. In problems where quasi-steady state is imposed at the final point, there is a higher number of subarcs than in problems where quasi-steady state is not imposed;the higher number of subarcs is due to the additional requirement that the lateral velocity and rudder angle vanish at the final point.

关键词： equations of motion kinematics dynamics hydrodynamics ship maneuvers optimal ship maneuvers course change maneuvers sidestep maneuvers control transformation singularity avoiding transformation sequential gradient-restoration algorithm

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Optimal control of a ship for collision avoidance maneuvers

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1999年第3期103卷 495-519页

作者： Miele, A Wang, T Chao, CS Dabney, JB Rice Univ Aeroastronaut Grp Houston TX 77251 USA Rice Univ Dept Mech Engn Houston TX 77251 USA

We consider a ship subject to kinematic, dynamic, and moment equations and steered via rudder under the assumptions that the rudder angle and rudder angle time rate are subject to upper and lower bounds. We formulate and solve four Chebyshev problems of optimal control, the optimization criterion being the maximization with respect to the state and control history of the minimum value with respect to time of the distance between two identical ships, one maneuvering and one moving in a predetermined way. Problems P1 and P2 deal with collision avoidance maneuvers without cooperation, while Problems P3 and P4 deal with collision avoidance maneuvers with cooperation. In Problems P1 and P3, the maneuvering ship must reach the final point with a given lateral distance, zero yaw angle, and zero yaw angle time rate. Sn Problems P2 and P4, the additional requirement of quasi-steady state is imposed at the final point. The above Chebyshev problems, transformed into Bolza problems via suitable transformations, are solved via the sequential gradient-restoration algorithm in conjunction with a new singularity avoiding transformation which accounts automatically for the bounds on rudder angle and rudder angle time rate. The optimal control histories involve multiple subarcs along which either the rudder angle is kept at one of the extreme positions or the rudder angle time rate is held at one of the extreme values. In problems where quasi-steady state is imposed at the final point, there is a higher number of subarcs than in problems where quasi-steady state is not imposed;the higher number of subarcs is due to the additional requirement that the lateral velocity and rudder angle vanish at the final point.

关键词： equations of motion kinematics dynamics hydrodynamics ship maneuvers optimal ship maneuvers collision avoidance maneuvers collision avoidance without cooperation collision avoidance with cooperation control transformation singularity avoiding transformation sequential gradient-restoration algorithm

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Optimal control of a ship for a course-changing maneuver

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1998年第2期97卷 281-297页

作者： Tzeng, CY Natl Taiwan Ocean Univ Inst Maritime Technol Keelung Taiwan

The steering control of a ship during a course-changing maneuver is formulated as a Bolza optimal control problem, which is solved via the sequential gradient-restoration algorithm (SGRA). Nonlinear differential equations describing the yaw dynamics of a steering ship are employed as the differential constraints, and both amplitude and slew rate limits on the rudder are imposed. Two performance indices are minimized: one measures the time integral of the squared course deviation between the actual ship course and a target course;the other measures the time integral of the absolute course deviation. Numerical results indicate that a smooth transition from the initial set course to the target course is achievable, with a trade-off between the speed of response and the amount of course angle overshoot.

关键词： nonlinear ship steering dynamics optimal control saturation slew rate limitation sequential gradient-restoration algorithm

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Optimal trajectories for Earth-to-Mars flight

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1997年第3期95卷 467-499页

作者： Miele, A Wang, T Rice Univ Aeroastron Grp Houston TX 77251 USA

This paper deals with the optimal transfer of a spacecraft from a low Earth orbit (LEG) to a low Mars orbit (LMO). The transfer problem is formulated via a restricted four-body model in that the spacecraft is considered subject to the gravitational fields of Earth, Mars, and Sun along the entire trajectory. This is done to achieve increased accuracy with respect to the method of patched conics. The optimal transfer problem is solved via the sequential gradient-restoration algorithm employed in conjunction with a variable-stepsize integration technique to overcome numerical difficulties due to large changes in the gravitational field near Earth and near Mars. The optimization criterion is the total characteristic velocity, namely, the sum of the velocity impulses at LEO and LMO. The major parameters are four: velocity impulse at launch, spacecraft vs. Earth phase angle at launch, planetary Mars/Earth phase angle difference at launch, and transfer time. These parameters must be determined so that Delta V is minimized subject to tangential departure from circular velocity at LEO and tangential arrival to circular velocity at LMO. For given LEO and LMO radii, a departure window can be generated by changing the planetary Mars/Earth phase angle difference at launch, hence changing the departure date, and then reoptimizing the transfer. This results in a one-parameter family of suboptimal transfers, characterized by large variations of the spacecraft vs. Earth phase angle at launch, but relatively small variations in transfer time and total characteristic velocity. For given LEO radius, an arrival window can be generated by changing the LMO radius and then recomputing the optimal transfer. This leads to a one-parameter family of optimal transfers, characterized by small variations of launch conditions, transfer time, and total characteristic velocity, a result which has important guidance implications. Among the members of the above one-parameter family, there is an optimu

关键词： flight mechanics astrodynamics celestial mechanics Earth-to-Mars missions departure window arrival window optimization sequential gradient-restoration algorithm

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UTILIZING AN ENGINEERING OPTIMIZATION APPROACH TO PREDICT MAXIMUM MASS-FLOW RATES OF STEAM AND WATER MIXTURES

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ENGINEERING OPTIMIZATION 1995年第4期23卷 267-285页

作者： LAM, TT [a] The Aerospace Corporation Los Angeles CA U.S.A

Two mass flux mathematical models for the study of critical single- and two-phase flows of water are formulated based on optimization theory. Analytical expressions for the mass flux functions are developed for the superheated vapor and saturated liquid-vapor mixtures (Homogeneous Equilibrium Model) by using the generalized equations of state. With the application of the general-purpose sequential gradient-restoration algorithm (SGRA), the mass flux is maximized for any given upstream stagnation flow condition. Furthermore, the thermodynamic properties at the exit plane are also determined simultaneously. The feasibility of this optimization technique is verified by comparing the results with those reported in the literature.

关键词： MULTIPHASE FLOW FLOW RATE ESTIMATION THERMODYNAMICS sequential gradient-restoration algorithm

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