A Chebyshev-Gauss Pseudospectral Method for Solving Optimal Control Problems

Tang, Xiaojun; Wei, Jianli; Chen, Kai

doi:10.1016/s1874-1029(15)30004-5

Cited by 8 publications

(3 citation statements)

References 18 publications

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“…During last decades, pseudospectral methods have been a research hotspot in the domain of trajectory optimization [8,9]. In this method, the control and state are firstly discretized at certain collocation points in the time interval of interest, which are then approximated by polynomial interpolation.…”

Section: Introductionmentioning

confidence: 99%

Trajectory Optimization Based on Multi‐Interval Mesh Refinement Method

Lei

Shao

Liu

et al. 2017

Mathematical Problems in Engineering

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In order to improve the optimization accuracy and convergence rate for trajectory optimization of the air-to-air missile, a multi-interval mesh refinement Radau pseudospectral method was introduced. This method made the mesh endpoints converge to the practical nonsmooth points and decreased the overall collocation points to improve convergence rate and computational efficiency. The trajectory was divided into four phases according to the working time of engine and handover of midcourse and terminal guidance, and then the optimization model was built. The multi-interval mesh refinement Radau pseudospectral method with different collocation points in each mesh interval was used to solve the trajectory optimization model. Moreover, this method was compared with traditional h method. Simulation results show that this method can decrease the dimensionality of nonlinear programming (NLP) problem and therefore improve the efficiency of pseudospectral methods for solving trajectory optimization problems.

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Section: Introductionmentioning

confidence: 99%

Trajectory Optimization Based on Multi‐Interval Mesh Refinement Method

Lei

Shao

Liu

et al. 2017

Mathematical Problems in Engineering

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“…According to references of dynamics modeling by Lie group [20,21] and optimal control with pseudospectral method [22,23], the matrix and vector operators can avoid triangle and antitriangle transformations which makes dynamics modeling easier. Pseudospectral method is a global numerical method which has high stability and is widely used in many domains, many engineering problems are solved successfully [24,25].…”

Section: Introductionmentioning

confidence: 99%

Kinematics, Dynamics, and Optimal Control of Pneumatic Hexapod Robot

Bai

Zeng

et al. 2017

Mathematical Problems in Engineering

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Pneumatic hexapod robot is driven by inert gas carried by itself, which has board application prospect in rescue operation of disaster conditions containing flammable gas. Cruising ability is main constraint for practical engineering application which is influenced by kinematics and dynamics character. The matrix operators and pseudospectral method are used to solve dynamics modeling and numerical calculation problem of robot under straight line walking. Kinematics model is numerically solved and relationship of body, joints, and drive cylinders is obtained. With dynamics model and kinematics boundary conditions, the optimal input gas pressure of leg swing and body moving in one step is obtained by pseudospectral method. According to action character of magnetic valve, calculation results of control inputs satisfy engineering design requirements, and cruising ability under finite gas is obtained.

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“…Computational methods for solving more general optimal control problems are also available; see, for example, [5,13,34,18,24,25,20,27,30,35] In 1992, Liao employed the basic ideas of the homotopy in topology to propose a general analytic method for non-linear problems, namely homotopy analysis method (HAM) [21]. This method has been used effectively to solve various non-linear problems in science and engineering such as Davey-Stewartson equation [11], Kawahara equations [1], and so on.…”

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confidence: 99%

A hybrid parametrization approach for a class of nonlinear optimal control problems

Vali¹,

Borzabadi²

2019

Numerical Algebra, Control &Amp; Optimization

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In this paper, a suitable hybrid iterative scheme for solving a class of non-linear optimal control problems (NOCPs) is proposed. The technique is based upon homotopy analysis and parametrization methods. Actually an appropriate parametrization of control is applied and state variables are computed using homotopy analysis method (HAM). Then performance index is transformed by replacing new control and state variables. The results obtained from the given method are compared with the results which are obtained using the spectral homotopy analysis method (SHAM), homotopy perturbation method (HPM), optimal homotopy perturbation method (OHPM), modified variational iteration method (MVIM) and differential transformations. The existence and uniqueness of the solution are presented. The comparison and ability of the given approach is illustrated via two examples.

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A Chebyshev-Gauss Pseudospectral Method for Solving Optimal Control Problems

Cited by 8 publications

References 18 publications

Trajectory Optimization Based on Multi‐Interval Mesh Refinement Method

Trajectory Optimization Based on Multi‐Interval Mesh Refinement Method

Kinematics, Dynamics, and Optimal Control of Pneumatic Hexapod Robot

A hybrid parametrization approach for a class of nonlinear optimal control problems

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