Conjugate gradient method with pseudospectral collocation scheme for optimal rocket landing guidance

Yang, Li; Chen, Wanchun; Zhang, Hao; Yang, Liang

doi:10.1016/j.ast.2020.105999

Cited by 23 publications

(7 citation statements)

References 28 publications

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“…In this section, the implementation process of the optimal guidance method in the case of general performance index and specific performance index ( 5) is given. The detailed derivation process of conjugate gradient and pseudospectral method is shown in reference [7].…”

Section: Optimal Guidance Methodsmentioning

confidence: 99%

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Optimal guidance method based on conjugate gradient method and pseudospectral method

Chen

Yang

2022

J. Phys.: Conf. Ser.

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This paper aims to propose a method to solve the nonlinear optimal guidance problems with various performance indexes. First, the conjugate gradient method is derived based on the performance indexes of general form and specified form, and the execution steps of the optimal guidance method are obtained. Secondly, the pseudospectral collocation scheme is used to solve some intermediate variables in the algorithm, and the differential equations are transformed into algebraic equations, so as to improve the computational efficiency. Finally, the proposed method is applied to the air-to-ground missile guidance problem. By comparing with the simulation results of GPOPS-II, the optimality of the proposed method is verified. Additionally, the high computational efficiency of the algorithm is also verified.

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Section: Optimal Guidance Methodsmentioning

confidence: 99%

“…This paper presents an optimal guidance method which can adapt to various performance indexes. This method is derived on the basis of pseudospectral collocation conjugate gradient method [7]. First, the mathematical description of air-to-ground missile guidance problem is given.…”

Section: Introductionmentioning

confidence: 99%

Optimal guidance method based on conjugate gradient method and pseudospectral method

Chen

Yang

2022

J. Phys.: Conf. Ser.

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“…2 Department of Mathematics, Sir Gurudas Mahavidyalaya, Kolkata 700067, India. 3 Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran. 4 DST-Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi 221005, India.…”

Section: Fundingmentioning

confidence: 99%

“…The conjugate gradient (CG) methods have played an important role in solving nonlinear optimization problems due to their simplicity of iteration and very low memory requirements [1,2]. Of course, the CG methods are not among the fastest or most robust optimization algorithms for solving nonlinear problems today, but they are very popular among engineers and mathematicians to solve nonlinear optimization problems [3][4][5]. The origin of the methods dates back to 1952 when Hestenes and Stiefel introduced a CG method [6] for solving a symmetric positive definite linear system of equations.…”

Section: Introductionmentioning

confidence: 99%

A q-Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization problems

et al. 2021

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A Polak–Ribière–Polyak (PRP) algorithm is one of the oldest and popular conjugate gradient algorithms for solving nonlinear unconstrained optimization problems. In this paper, we present a q-variant of the PRP (q-PRP) method for which both the sufficient and conjugacy conditions are satisfied at every iteration. The proposed method is convergent globally with standard Wolfe conditions and strong Wolfe conditions. The numerical results show that the proposed method is promising for a set of given test problems with different starting points. Moreover, the method reduces to the classical PRP method as the parameter q approaches 1.

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“…As an important part of modern control theory, optimal control has been widely applied in many practical engineering fields such as aerospace, 1–3 robotics, 4 and transportation 5 . Taking the aerospace field as an example, the soft landing of the detector on the planet, the re‐entry guidance of the vehicle, the orbit transfer of the spacecraft and so on can be regarded as the optimal control problems (OCPs).…”

Section: Introductionmentioning

confidence: 99%

Successive Chebyshev pseudospectral convex optimization method for nonlinear optimal control problems

Chen

Yang

2021

Intl J Robust & Nonlinear

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This article aims at proposing a successive Chebyshev pseudospectral convex optimization method for solving general nonlinear optimal control problems (OCPs). First, Chebyshev pseudospectral discrete scheme is used to discretize a general nonlinear OCP. At the same time, a convex subproblem is formulated by using the first‐order Taylor expansion to convexify the discretized nonlinear dynamic constraints. Second, a trust‐region penalty term is added to the performance index of the subproblem, and a successive convex optimization algorithm is proposed to solve the subproblem iteratively. Noted that the trust‐region penalty parameters can be adjusted according to the linearization error in iterative process, which improves convergence rate. Third, the Karush–Kuhn–Tucker conditions of the subproblem are derived, and furthermore, a proof is given to show that the algorithm will iteratively converge to the subproblem. Additionally, the global convergence of the algorithm is analyzed and proved, which is based on three key lemmas. Finally, the orbit transfer problem of spacecraft is used to test the performance of the proposed method. The simulation results demonstrate the optimal control is bang‐bang form, which is consistent with the result of theoretical proof. Also, the algorithm is of efficiency, fast convergence rate, and high accuracy. Therefore, the proposed method provides a new approach for solving nonlinear OCPs online and has great potential in engineering practice.

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Conjugate gradient method with pseudospectral collocation scheme for optimal rocket landing guidance

Cited by 23 publications

References 28 publications

Optimal guidance method based on conjugate gradient method and pseudospectral method

Optimal guidance method based on conjugate gradient method and pseudospectral method

A q-Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization problems

Successive Chebyshev pseudospectral convex optimization method for nonlinear optimal control problems

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