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PROPERTIES OF THE sequential gradient-restoration algorithm (SGRA) .1. INTRODUCTION AND COMPARISON WITH RELATED METHODS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1989年第1期62卷 77-98页

作者： ROM, M AVRIEL, M 1.Faculty of Industrial Engineering and Management Technion Israel Institute of Technology Haifa Israel

The sequential gradient-restoration algorithm (SGRA) was developed in the late 1960s for the solution of equality-constrained nonlinear programs and has been successfully implemented by Miele and coworkers on many large-scale problems. The algorithm consists of two major sequentially applied phases. The first is a gradient-type minimization in a subspace tangent to the constraint surface, and the second is a feasibility restoration procedure. In Part 1, the original SGRA algorithm is described and is compared with two other related methods: the gradient projection and the generalized reduced gradient methods. Next, the special case of linear equalities is analyzed. It is shown that, in this case, only the gradient-type minimization phase is needed, and the SGRA becomes identical to the steepest-descent method. Convergence proofs for the nonlinearly constrained case are given in Part 2.

关键词： sequential gradient-restoration algorithm nonlinear programming gradient-type optimization feasibility restoration

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PROPERTIES OF THE OPTIMAL TRAJECTORIES FOR COPLANAR, AEROASSISTED ORBITAL TRANSFER

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1991年第1期69卷 1-30页

作者： MIELE, A WANG, T DEATON, AW NASA GEORGE C MARSHALL SPACE FLIGHT CTRSYST ANAL & INTEGRAT LABFLIGHT MECH BRANCHHUNTSVILLEAL 35812

This paper is concerned with the optimization of trajectories for coplanar, aeroassisted orbital transfer (AOT) from a high Earth orbit (HEO) to a low Earth orbit (LEO). In particular, HEO can be a geosynchronous Earth orbit (GEO). It is assumed that the initial and final orbits are circular, that the gravitational field is central and is governed by the inverse square law, and that two impulses are employed, one at HEO exit and one at LEO entry. During the atmospheric pass, the trajectory is controlled via the lift coefficient in such a way that the total characteristic velocity is minimized. First, an ideal optimal trajectory is determined analytically for lift coefficient unbounded. This trajectory is called grazing trajectory, because the atmospheric pass is made by flying at constant altitude along the edge of the atmosphere until the excess velocity is depleted. For the grazing trajectory, the lift coefficient varies in such a way that the lift, the centrifugal force due to the Earth's curvature, the weight, and the Coriolis force due to the Earth's rotation are in static balance. Also, the grazing trajectory minimizes the total characteristic velocity and simultaneously nearly minimizes the peak values of the altitude drop, the dynamic pressure, and the heating rate. Next, starting from the grazing trajectory results, a real optimal trajectory is determined numerically for lift coefficient bounded from both below and above. This trajectory is characterized by atmospheric penetration with the smallest possible entry angle, followed by flight at the lift coefficient lower bound. Consistently with the grazing trajectory behavior, the real optimal trajectory minimizes the total characteristic velocity and simultaneously nearly minimizes the peak values of the altitude drop, the dynamic pressure, and the heating rate.

关键词： FLIGHT MECHANICS ASTRODYNAMICS AEROASSISTED ORBITAL TRANSFER OPTIMAL TRAJECTORIES NONLINEAR 2-POINT BOUNDARY-VALUE PROBLEMS sequential gradient-restoration algorithm

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DECOMPOSITION TECHNIQUE AND OPTIMAL TRAJECTORIES FOR THE AEROASSISTED FLIGHT EXPERIMENT

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1991年第2期69卷 201-234页

作者： MIELE, A WANG, T DEATON, AW NASA GEORGE C MARSHALL SPACE FLIGHT CTRSYST ANAL & INTEGRAT LABFLIGHT MECH BRANCHHUNTSVILLEAL 35812

The aeroassisted flight experiment (AFE) refers to a spacecraft to be launched and then recovered by the space shuttle in 1994. It simulates a transfer from a geosynchronous Earth orbit (GEO) to a low Earth orbit (LEO). Specifically, the AFE spacecraft is released from the space shuttle and is accelerated by means of a solid rocket motor toward Earth, so as to achieve atmospheric entry conditions close to those of a spacecraft returning from GEO. Following the atmospheric pass, the AFE spacecraft ascends to the specified LEO via an intermediate parking Earth orbit (PEO). The final maneuver includes the rendezvous with and the capture by the space shuttle. The entry and exit orbital planes of the AFE spacecraft are identical with the orbital plane of the space shuttle. In this paper, with reference to the AFE spacecraft, an actual GEO-to-LEO transfer is considered and optimal trajectories are determined by minimizing the total characteristic velocity. The optimization is performed with respect to the time history of the controls (angle of attack and angle of bank), the entry path inclination and the flight time being free. Two transfer maneuvers are considered: (DA) direct ascent to LEO;(IA) indirect ascent to LEO via PEO. While the motion of the AFE spacecraft in a 3D-space is described by a system of six ODEs, substantial simplifications are possible if one exploits these facts: (i) the instantaneous orbital plane is nearly identical with the initial orbital plane;(ii) the bank angle is small;and (iii) the Earth's angular velocity is relatively small. Under these assumptions, the complete system can be decoupled into two subsystems, one describing the longitudinal motion and one describing the lateral motion. The angle of attack history, the entry path inclination, and the flight time are determined via the longitudinal motion subsystem;in this subsystem, the total characteristic velocity is minimized subject to the specified LEO requirement. The angle of bank hist

关键词： Flight mechanics astrodynamics hypervelocity flight aeroassisted orbital transfer aeroassisted flight experiment optimal trajectories guidance trajectories decomposition techniques longitudinal motion lateral motion sequential gradient-restoration algorithm nonlinear two-point boundary-value problems

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APPLICATION OF THE sequential gradient-restoration algorithm TO THERMAL CONVECTIVE INSTABILITY PROBLEMS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1986年第1期49卷 47-63页

作者： LAM, TT BAYAZITOGLU, Y 1.Department of Mechanical Engineering and Materials Science Rice University Houston Texas

The problem of the thermal stability of a horizontal incompressible fluid layer with linear and nonlinear temperature distributions is solved by using the sequential gradient-restoration algorithm developed for optimal control problems. The hydrodynamic boundary conditions for the layer include a rigid or free upper surface and a rigid lower surface. The resulting disturbing equations are solved as a Bolza problem in the calculus of variations. The results of the study are compared with the existing works in the literature.

关键词： Convective instability thermal instability Benard problem linear stability theory optimal control numerical methods computing methods gradient methods gradient-restoration algorithm sequential gradient-restoration algorithm

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NEIGHBORING EXTREMALS OF DYNAMIC OPTIMIZATION PROBLEMS WITH PATH EQUALITY CONSTRAINTS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1988年第3期57卷 519-536页

作者： LEE, AY STANFORD UNIV STANFORDCA 94305

Neighboring extremals of dynamic optimization problems with path equality constraints and with an unknown parameter vector are considered in this paper. With some simplifications, the problem is reduced to solving a linear, time-varying two-point boundary-value problem with integral path equality constraints. A modified backward sweep method is used to solve this problem. Two example problems are solved to illustrate the validity and usefulness of the solution technique.

关键词： sequential gradient-restoration algorithm backward sweep method path equality constraints second variation neighboring optimal feedback laws

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QUASI-STEADY FLIGHT TO QUASI-STEADY FLIGHT TRANSITION FOR ABORT LANDING IN A WINDSHEAR - TRAJECTORY OPTIMIZATION AND GUIDANCE

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1988年第2期58卷 165-207页

作者： MIELE, A WANG, T MELVIN, WW DELTA AIRLINES ATLANTAGA AIR LINE PILOTS ASSOC COMM AIRWORTHINESS & PERFORMANCEWASHINGTONDC

This paper is concerned with the optimal transition and the near-optimum guidance of an aircraft from quasi-steady flight to quasi-steady flight in a windshear. The abort landing problem is considered with reference t... 详细信息

关键词： Flight mechanics abort landing quasi-steady flight to quasi-steady flight transition optimal trajectories optimal control guidance strategies acceleration guidance gamma guidance feedback control windshear problems sequential gradient-restoration algorithm dual sequential gradient-restoration algorithm

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OPTIMAL PENETRATION LANDING TRAJECTORIES IN THE PRESENCE OF WINDSHEAR

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1988年第1期57卷 1-40页

作者： MIELE, A WANG, T WANG, H MELVIN, WW DELTA AIRLINES ATLANTAGA AIR LINE PILOTS ASSOC AIRWORTHINESS & PERFORMANCE COMMWASHINGTONDC

This paper is concerned with optimal flight trajectories in the presence of windshear. The penetration landing problem is considered with reference to flight in a vertical plane, governed by either one control (the angle of attack, if the power setting is predetermined) or two controls (the angle of attack and the power setting). Inequality constraints are imposed on the angle of attack, the power setting, and their time derivatives.

关键词： Flight mechanics landing abort landing penetration landing optimal trajectories optimal control windshear problems sequential gradient-restoration algorithm primal sequential gradient-restoration algorithm

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OPTIMAL TRAJECTORIES FOR LEO-TO-LEO AEROASSISTED ORBITAL TRANSFER

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ACTA ASTRONAUTICA 1988年第C期18卷 99-122页

作者： MIELE, A LEE, WY MEASE, KD Aero-Astronautics Group Rice University Houston Texas Jet Propulsion Laboratory Pasadena California USA

This paper considers both classical and minimax problems of optimal control arising in the study of noncoplanar, aeroassisted orbital transfer. The maneuver considered involves the transfer from one planetary orbit to another having different orbital inclination, but the same radius. An example is the LEO-to-LEO transfer of a spacecraft with a prescribed plane change, where LEO denotes low Earth orbit. The basic idea is to employ the hybrid combination of propulsive maneuvers in space and aerodynamic maneuvers in the sensible atmosphere. Hence, this type of flight is also called synergetic space flight. With reference to the atmospheric part of the maneuver, trajectory control is achieved by modulating the lift coefficient (hence, the angle of attack) and the angle of bank. The presence of upper and lower bounds on the lift coefficient is considered. Three different transfer maneuvers are studied. Type 1 involves four impulses and four space plane changes; Type 2 involves three impulses and three space plane changes; and Type 3 involves three impulses and no space plane change. In Type 1, the initial impulse directs the spacecraft away from Earth, and then is followed by an apogee impulse propelling the spacecraft toward Earth; in Types 2 and 3, the initial impulse directs the spacecraft toward Earth. A common element of these maneuvers is that they all include an atmospheric pass, with velocity depletion coupled with plane change. Within the framework of classical optimal control, the following problems are studied: (P1) minimize the energy required for orbital transfer; (P4) maximize the time of flight during the atmospheric portion of the trajectory; (P5) minimize the time integral of the square of the path inclination. Within the framework of minimax optimal control, the following problem is studied: (Q1) minimize the peak heating rate. Numerical solutions for Problems (P1), (P4), (P5), (Q1) are obtained by means of the sequential gradient-restoration algorithm

关键词： Orbital transfer coplanar orbital transfer noncoplanar orbital transfer LEO-to-LEO transfer aeroassisted orbital transfer transfer between circular orbits plane change lift coefficient modulation angle of bank modulation optimal trajectories optimal control problems minimax problems Bolza problems Chebyshev problems transformation techniques numerical methods computing methods sequential gradient-restoration algorithm

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DYNAMIC OPTIMIZATION PROBLEMS WITH BOUNDED TERMINAL CONDITIONS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1987年第1期52卷 151-162页

作者： LEE, AY STANFORD UNIV STANFORDCA 94305

Bounded terminal conditions of nonlinear optimization problems are converted to equality terminal conditions via the Valentine's device. In so doing, additional unknown parameters are introduced into the problem. The transformed problems can still be easily solved using the sequential gradient-restoration algorithm (SGRA) via a simple augmentation of the unknown parameter vector π. Three example problems with bounded terminal conditions are solved to verify this technique.

关键词： sequential gradient-restoration algorithm nonlinear optimization problems bounded terminal conditions Valentine's device

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OPTIMAL ABORT LANDING TRAJECTORIES IN THE PRESENCE OF WINDSHEAR

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1987年第2期55卷 165-202页

作者： MIELE, A WANG, T TZENG, CY MELVIN, WW DELTA AIRLINES ATLANTAGA AIR LINE PILOTS ASSOC AIRWORTHINESS & PERFORMANCE COMMWASHINGTONDC

This paper is concerned with optimal flight trajectories in the presence of windshear. The abort landing problem is considered with reference to flight in a vertical plane. It is assumed that, upon sensing that the airplane is in a windshear, the pilot increases the power setting at a constant time rate until maximum power setting is reached; afterward, the power setting is held constant. Hence, the only control is the angle of attack. Inequality constraints are imposed on both the angle of attack and its time derivative.

关键词： Flight mechanics landing abort landing penetration landing optimal trajectories optimal control windshear problems sequential gradient-restoration algorithm dual sequential gradient-restoration algorithm

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