International Journal of Control

2019

DOI: 10.1080/00207179.2019.1638970

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Gradient method using pseudospectral collocation scheme for two-stage optimal control with an unspecified switching time

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Cited by 6 publications

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References 33 publications

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“…At present, there are some works that combine the pseudospectral method with the gradient method to achieve higher efficiency. In Reference 26, a two‐stage gradient method was proposed. To obtain faster calculation speed, the pseudospectral collocation scheme is used to solve the influence function in the gradient method.…”

Section: Introductionmentioning

confidence: 99%

Successive Chebyshev pseudospectral convex optimization method for nonlinear optimal control problems

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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.

“…At present, there are some works that combine the pseudospectral method with the gradient method to achieve higher efficiency. In Reference 26, a two‐stage gradient method was proposed. To obtain faster calculation speed, the pseudospectral collocation scheme is used to solve the influence function in the gradient method.…”

Section: Introductionmentioning

confidence: 99%

Successive Chebyshev pseudospectral convex optimization method for nonlinear optimal control problems

¹

,

²

,

³

2021

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

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.

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

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Aerospace Science and Technology

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Suboptimal Impact-Angle-Constrained Guidance Law Using Linear Pseudospectral Model Predictive Spread Control

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2020

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This paper aims at proposing a nonlinear suboptimal impact-angle-constrained guidance law for an interceptor engaging against an incoming high-speed ballistic missile in three dimensions. The method is based on an improved Linear Pseudospectral Model Predictive Control (LPMPC), in which the control variable is parameterized as a sum of general standard basis functions with few undetermined coefficients. Although the final solution is suboptimal, a series of analytical improved formulas can be also successively derived to eliminate the final predictive errors, which remains the character that few points will achieve high accuracy. Furthermore, the number of improved variables will significantly decrease, which will further improve the computational efficiency and provide smoother control history. Several numerical simulations are carried out to evaluate the performance of the proposed method. Results show that it performs well in achieving desired impact angles and the near-zero miss distance with high accuracy. In comparison with other typical methods, the proposed method has superior performance in computational efficiency. Therefore, it has the potential to be applied in the framework of guidance.

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