Autonomous entry guidance using Linear Pseudospectral Model Predictive Control

Yang, Liang; Liu, Xiaoming; Chen, Wanchun; Zhang, Hao

doi:10.1016/j.ast.2018.06.031

Cited by 34 publications

(8 citation statements)

References 31 publications

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“…where λ i , η j are the KKT multipliers associated with equality and inequality constraints, respectively. The optimal solution,X, is determined by the gradient of the augmented cost function [33]. If J, g, and m are continuously differentiable functions, and then there exists KKT multipliers λ and μ such that…”

Section: Derivation Of the Kkt Conditionsmentioning

confidence: 99%

“…In addition, the terminal position of Lambert's problem is no longer a given constant in the MVIP, but is determined on the orbit of the target as formulated in g 1 . Thus, f M is involved in the third equation of equation (33), which also decreases the computational difficulty. Therefore, the independent variables in the equality constraint g 2 are set to be X = t, P, f M T , which is different from that in equation (23).…”

Section: Derivation Of the Kkt Conditionsmentioning

confidence: 99%

“…At the beginning, substituting equations (2) and (24) into equation (33) and introducing a set of notations…”

Section: Partialmentioning

confidence: 99%

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Optimal Midcourse Guidance Algorithm for Exoatmospheric Interception Using Analytical Gradients

Chen

Yang

et al. 2019

International Journal of Aerospace Engineering

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This paper is aimed at providing a semianalytical method to solve the optimal exoatmospheric interception problem with the minimum fuel consumption. A nonlinear programming (NLP) problem with the minimum velocity increment, which involves Lambert’s problem with unspecified time-of-flight, is firstly formulated. Then, a set of Karush-Kuhn-Tucker conditions and the Jacobian matrix corresponding to those conditions are derived in an analytical manner, even though the derivatives are mathematically complicated and computationally onerous. Therefore, the Newton-Raphson method can be used to efficiently solve this problem. To further decrease computational cost, a near-optimal initialization method reducing the dimension of the search space is presented to provide a better initial guess. The performance of the proposed method is assessed by numerical experiments and comparison with other methods. The results show that this method is not only of high computational efficiency and accuracy but also applicable to onboard guidance.

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Section: Derivation Of the Kkt Conditionsmentioning

confidence: 99%

Section: Derivation Of the Kkt Conditionsmentioning

confidence: 99%

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Optimal Midcourse Guidance Algorithm for Exoatmospheric Interception Using Analytical Gradients

Chen

Yang

et al. 2019

International Journal of Aerospace Engineering

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“…Then, the TPBVP is transformed into a set of linear algebraic equations by Gauss pseudospectral collocation. This method has high efficiency and accuracy, and has been further developed and applied 18,19 . Similarly, symplectic pseudospectral method is also a new method for solving nonlinear OCPs with complicated factors, which has a good application prospect 20–24 .…”

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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“…PSM has been extensively used in literature to solve a wide range of optimal control problems involving large mechanisms (Gong et al, 2007) to small systems (Li et al, 2011) alike. A wide variety of other challenging control problems in aerospace and autonomous systems (Banerjee et al, 2019a, 2019b; Chai et al, 2015; Fahroo and Ross, 2002; Kang and Bedrossian, 2007; Yang et al, 2017, 2018), as well as for underwater glider (Kraus, 2010) has also been solved using PSM. The application of PSM is not only limited to theory, but it has also been successfully applied to perform attitude maneuvers of the International Space Station (Bedrossian et al, 2009) and a minimum-time rotational maneuver for the space telescope called TRACE (Karpenko et al, 2011, 2012).…”

Section: Introductionmentioning

confidence: 99%

Time-energy optimal guidance strategy for realistic interceptor using pseudospectral method

Banerjee

Nabi

Raghunathan

2020

Transactions of the Institute of Measurement and Control

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This paper proposes the use of Legendre pseudospectral method (PSM) to obtain the optimal guidance strategy for a two-dimensional interceptor problem. An optimal control problem is formulated that addresses the conflicting objective of minimizing the energy usage, along with minimizing the time taken by missile to capture the target. The PSM-based guidance strategy is compared with other conventional guidance laws such as pure proportional navigation (PPN) guidance law and also evolutionary algorithm inspired differential evolution tuned proportional navigation (DEPN) guidance law. A scheme by which the PSM guidance strategy can be applied online is also included in this paper. The cost function value and the interception time indicates the superiority of the PSM-based guidance strategy.

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Autonomous entry guidance using Linear Pseudospectral Model Predictive Control

Cited by 34 publications

References 31 publications

Optimal Midcourse Guidance Algorithm for Exoatmospheric Interception Using Analytical Gradients

Optimal Midcourse Guidance Algorithm for Exoatmospheric Interception Using Analytical Gradients

Successive Chebyshev pseudospectral convex optimization method for nonlinear optimal control problems

Time-energy optimal guidance strategy for realistic interceptor using pseudospectral method

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