Costate Estimation using Multiple-Interval Pseudospectral Methods

Darby, Christopher L.; Garg, Divya; Rao, Anil V.

doi:10.2514/1.55717

Cited by 7 publications

(9 citation statements)

References 20 publications

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“…Convergence in an h method is then achieved by increasing the number and placement of the mesh points Jain and Tsiotras 2008;Zhao and Tsiotras 2011]. More recently, a great deal of research as been done in the class of direct Gaussian quadrature orthogonal collocation methods [Benson et al 2006;Darby et al 2011a;Elnagar and Razzaghi 1998;Elnagar et al 1995;Garg et al 2010Garg et al , 2011aGarg et al , 2011bGong et al 2008b;Huntington and Rao 2008;Huntington et al 2007; Kameswaran and Biegler 2008;Patterson and Rao 2012;Rao et al 2010]. In a Gaussian quadrature collocation method, the state is typically approximated using a Lagrange polynomial where the support points of the Lagrange polynomial are chosen to be points associated with a Gaussian quadrature.…”

Section: Introductionmentioning

confidence: 99%

Gpops-Ii

Patterson

Rao

2014

ACM Trans. Math. Softw.

Self Cite

848

109

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A general-purpose MATLAB software program called GPOPS − II is described for solving multiple-phase optimal control problems using variable-order Gaussian quadrature collocation methods. The software employs a Legendre-Gauss-Radau quadrature orthogonal collocation method where the continuous-time optimal control problem is transcribed to a large sparse nonlinear programming problem (NLP). An adaptive mesh refinement method is implemented that determines the number of mesh intervals and the degree of the approximating polynomial within each mesh interval to achieve a specified accuracy. The software can be interfaced with either quasi-Newton (first derivative) or Newton (second derivative) NLP solvers, and all derivatives required by the NLP solver are approximated using sparse finite-differencing of the optimal control problem functions. The key components of the software are described in detail and the utility of the software is demonstrated on five optimal control problems of varying complexity. The software described in this article provides researchers a useful platform upon which to solve a wide variety of complex constrained optimal control problems. ACM Reference Format:Patterson, M. A. and Rao, A. V. 2012. GPOPS-II: A MATLAB software for solving multiple-phase optimal control problems using hp-adaptive Gaussian quadrature collocation methods and sparse nonlinear programming.

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Section: Introductionmentioning

confidence: 99%

Gpops-Ii

Patterson

Rao

2014

ACM Trans. Math. Softw.

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848

109

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“…The costate estimation in optimal control problems also uses hp-method [66]. The stopping criterion, new polynomial degree, and locations of the new mesh points are improved for robustness and fast convergence.…”

Section: Fig 6 Comparisons Of Dps and Cps For The H-methods And P-methodsmentioning

confidence: 99%

Progress in reentry trajectory planning for hypersonic vehicle

Zhao

Zhou

Jin

2014

J. of Syst. Eng. Electron.

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The reentry trajectory planning for hypersonic vehicles is critical and challenging in the presence of numerous nonlinear equations of motion and path constraints, as well as guaranteed satisfaction of accuracy in meeting all the specified boundary conditions. In the last ten years, many researchers have investigated various strategies to generate a feasible or optimal constrained reentry trajectory for hypersonic vehicles. This paper briefly reviews the new research efforts to promote the capability of reentry trajectory planning. The progress of the onboard reentry trajectory planning, reentry trajectory optimization, and landing footprint is summarized. The main challenges of reentry trajectory planning for hypersonic vehicles are analyzed, focusing on the rapid reentry trajectory optimization, complex geographic constraints, and cooperative strategies.

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“…However, any method appropriate to the approximate problem established in Section 3, Problem P M , can be applied to the time domain. Discretized state and control constraints ( 14) -( 18) may create an approximate problem which, due to the constraints, may benefit from a method from a time domain method which caters more specifically to constrained optimal control problems, such as the local pseudospectral method [Darby, Garg, and Rao (2011)], or the symplectic pseudospectral method [Wang, Peng, Zhang, Chen, and Zhong (2017)]. This can be ascertained from the structure of Problem P. In this example, which has smooth state and control solutions, we find the global pseudospectral method utilized to be sufficient.…”

Section: Example: Optimal Searchmentioning

confidence: 99%

Consistent numerical methods for state and control constrained trajectory optimisation with parameter dependency

Walton

Kaminer

Gong

2020

International Journal of Control

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This paper describes and proves the consistency of a flexible numerical method for producing solutions to state and control constrained control problems with parameter dependencies. This method allows for the use of a variety of underlying discretization schemes, which can be catered to differing numerical challenges of specific problems, such as rapid convergence or large parameter spaces. The paper first provides a broad formulation for optimal control problems with parameter dependencies which includes multiple types of state, control, and end time constraints to enable a wide scope of application. For this formulation, the consistency of these methods for state and control constrained problems is then proved. Finally, a numerical example of an optimal search problem with constraints is demonstrated.

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Costate Estimation using Multiple-Interval Pseudospectral Methods

Cited by 7 publications

References 20 publications

Gpops-Ii

Gpops-Ii

Progress in reentry trajectory planning for hypersonic vehicle

Consistent numerical methods for state and control constrained trajectory optimisation with parameter dependency

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