Sequential conjugate gradient-restoration algorithm for optimal control problems with nondifferential constraints, † Part I

Miele, A.; Cloutier, J.R.; Mohanty, B.P.; Wu, A. K.

doi:10.1080/00207177908922693

Cited by 13 publications

(1 citation statement)

References 6 publications

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“…Also, state and control variables between these systems can be continuous or discontinuous. This algorithm is an expansion and a development of SGRA, [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] which has been designed to obtain smaller performance index during a repetitive cycle. This cycle is two-phased and it includes gradient phase and restoration phase.…”

Section: The Summary Of Calculation Process Of Optimal Control M-sgramentioning

confidence: 99%

Optimal guidance of spacecraft rendezvous via free initial velocity vector

Saghamanesh

Novinzadeh

2013

Proceedings of the Institution of Mechanical Engineers, Part G:

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In this research, we focus on an optimal trajectory of a spacecraft rendezvous operation. This optimal trajectory, which is studied in rendezvous problem consists of a controlling distribution, parametric and permitted forms of performance index of minimum fuel-time free; this method will guide the chaser spacecraft toward the target spacecraft in optimal trajectory by using multiple-subarc sequential gradient–restoration algorithm. During trajectory analysis, we will define two problems, P1 and P2. In P1, initial position vector and initial velocity vector are given and fixed and in P2, initial position vector is given and fixed, while initial velocity vector varies and will be free. Previous studies show that the condition of optimal fuel in a solution will be obtained with four subarcs and it shows that for distribution of optimal thrust, the amount of maximum thrust or zero during each subarc will be needed. The main result is that, the new method proposed by this study leads to reduction in performance index and also fuel consumption will be in an appropriate amount. This event takes place in proportion of initial free velocity (problem P2) to initial fixed velocity (problem P1). Another result is that the reduction in fuel consumption and performance index is associated with a remarkable reduction in central processing unit time up to 1650 order. The result of this investigation for rendezvous mission between target spacecraft and chaser spacecraft named OCAT1.1 was extracted and examined on SuperCluster computer.

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Section: The Summary Of Calculation Process Of Optimal Control M-sgramentioning

confidence: 99%

Optimal guidance of spacecraft rendezvous via free initial velocity vector

Saghamanesh

Novinzadeh

2013

Proceedings of the Institution of Mechanical Engineers, Part G:

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Sequential conjugate gradient‐restoration algorithm for optimal control problems with non‐differential constraints and general boundary conditions, part I

Miele

1980

Optim Control Appl Methods

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In this paper, a new member of the family of sequential gradient‐restoration algorithms for the solution of optimal control problems is presented. This is an algorithm of the conjugate gradient type, which is designed to solve two classes of optimal control problems, called Problem P1 and Problem P2 for easy indentification. Problem P1 involves minimizing a functional I subject to differential constraints and general boundary conditions. It consists of finding the state x(t), the control u(t), and the parameter pi so that the functional I is minimized, while the constraints and the boundary conditions are satisfied to a predetermined accuracy. Problem P2 extends Problem P1 to include non‐differential constraints to be satisfied everywhere along the interval of integration. The approach taken is a sequence of two‐phase cycles, composed of a conjugate gradient phase and a restoration phase. The conjugate gradient phase involves one iteration and is designed to decrease the value of the functional, while the constraints are satisfied to first order. The restoration phase involves one or more iterations; each restorative iteration is designed to force constraint satisfaction to first order, while the norm squared of the variations of the control, the parameter, and the missing components of the initial state is minimized. The resulting algorithm has several properties: (i) it produces a sequence of feasible solutions; (ii) each feasible solution is characterized by a value of the functional I which is smaller than that associated with any previous feasible solution; and (iii) for the special case of a quadratic functional subject to linear constraints, the variations of the state, control, and parameter produced by the sequence of conjugate gradient phases satisfy various orthogonality and conjugacy conditions. The algorithm presented here differs from those of References 1‐4, in that it is not required that the state vector be given at the initial point. Instead, the initial conditions can be absolutely general. In analogy with References 1‐4, the present algorithm is capable of handling general final conditions; therefore, it is suitable for the solution of optimal control problems with general boundary conditions. The importance of the present algorithm lies in that many optimal control problems either arise naturally in the present format or can be brought to such a format by means of suitable transformations.5 Therefore, a great variety of optimal control problems can be handled. This includes: (i) problems with control equality constraints, (ii) problems with state equality constraints, (iii) problems with state‐derivative equality constraints, (iv) problems with‐control inequality constraints, (v) problems with state inequality constraints, (vi) problems with state‐derivative inequality constraints, and (vii) Chebyshev minimax problems. Several numerical examples are presented in Part 2 (Reference 6) in order to illustrate the performance of the algorithm associated with Problem P1 and Problem P2. The...

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SEQUENTIAL CONJUGATE GRADIENT-RESTORATION ALGORITHM FOR OPTIMAL CONTROL PROBLEMS WITH NONDIFFERENTIAL CONSTRAINTS11This research was supported by the Office of Scientific Research, Office of Aerospace Research, United States Air Force, Grant No. AF-AFOSR-76-3075. This paper is based on the investigations presented in Refs. 1–2.

Miele

Cloutier

1979

Applied Nonlinear Analysis

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Sequential conjugate gradient-restoration algorithm for optimal control problems with nondifferential constraints, † Part I

Cited by 13 publications

References 6 publications

Optimal guidance of spacecraft rendezvous via free initial velocity vector

Optimal guidance of spacecraft rendezvous via free initial velocity vector

Sequential conjugate gradient‐restoration algorithm for optimal control problems with non‐differential constraints and general boundary conditions, part I

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