Research output: Contribution to journal › Article › peer-review

**A self-stabilizing Pantoja-like indirect algorithm for optimal control.** / Christianson, B.

Research output: Contribution to journal › Article › peer-review

Christianson, B 2001, 'A self-stabilizing Pantoja-like indirect algorithm for optimal control', *Optimization Methods and Software*, vol. 16, no. 1-4, pp. 131-149. https://doi.org/10.1080/10556780108805833

Christianson, B. (2001). A self-stabilizing Pantoja-like indirect algorithm for optimal control. *Optimization Methods and Software*, *16*(1-4), 131-149. https://doi.org/10.1080/10556780108805833

Christianson B. A self-stabilizing Pantoja-like indirect algorithm for optimal control. Optimization Methods and Software. 2001;16(1-4):131-149. https://doi.org/10.1080/10556780108805833

@article{c639bede2b7746eb812bea2f68416d65,

title = "A self-stabilizing Pantoja-like indirect algorithm for optimal control",

abstract = "In 1983 Pantoja described a computationally efficient stagewise construction of the Newton direction for the discrete time optimal control problem. Automatic Differentiation can be used to implement Pantoja's algorithm and calculate the Newton direction, without truncation error, and without extensive manual re-writing of targetfunction code to form derivatives. Pantoja's algorithm is direct, in that the independent variables are the control vectors at each timestep. In this paper we formulate an indirect analogue of Pantoja's algorithm, in which the only independent variables are the components of a costate vector corresponding to the initial timestep. This reformulated algorithm gives exactly the Newton step for the initial costate with respect to a terminal transversality condition: at each timestep we solve implicit equations for the current controlsand successor costates. A remarkable feature of the indirect algorithm is that it is straiehtforward to comensate for the effect of non-zero residuals in the implicit costate equations. .The indirect reformulation of Pantoja's algorithm set out in this paper is a suitable basis for verified optimization using interval methods.",

author = "B. Christianson",

note = "Original article can be found at: http://www.informaworld.com/smpp/title~content=t713645924 Copyright Taylor and Francis / Informa.",

year = "2001",

doi = "10.1080/10556780108805833",

language = "English",

volume = "16",

pages = "131--149",

journal = "Optimization Methods and Software",

issn = "1055-6788",

publisher = "Taylor and Francis Ltd.",

number = "1-4",

}

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T1 - A self-stabilizing Pantoja-like indirect algorithm for optimal control

AU - Christianson, B.

N1 - Original article can be found at: http://www.informaworld.com/smpp/title~content=t713645924 Copyright Taylor and Francis / Informa.

PY - 2001

Y1 - 2001

N2 - In 1983 Pantoja described a computationally efficient stagewise construction of the Newton direction for the discrete time optimal control problem. Automatic Differentiation can be used to implement Pantoja's algorithm and calculate the Newton direction, without truncation error, and without extensive manual re-writing of targetfunction code to form derivatives. Pantoja's algorithm is direct, in that the independent variables are the control vectors at each timestep. In this paper we formulate an indirect analogue of Pantoja's algorithm, in which the only independent variables are the components of a costate vector corresponding to the initial timestep. This reformulated algorithm gives exactly the Newton step for the initial costate with respect to a terminal transversality condition: at each timestep we solve implicit equations for the current controlsand successor costates. A remarkable feature of the indirect algorithm is that it is straiehtforward to comensate for the effect of non-zero residuals in the implicit costate equations. .The indirect reformulation of Pantoja's algorithm set out in this paper is a suitable basis for verified optimization using interval methods.

AB - In 1983 Pantoja described a computationally efficient stagewise construction of the Newton direction for the discrete time optimal control problem. Automatic Differentiation can be used to implement Pantoja's algorithm and calculate the Newton direction, without truncation error, and without extensive manual re-writing of targetfunction code to form derivatives. Pantoja's algorithm is direct, in that the independent variables are the control vectors at each timestep. In this paper we formulate an indirect analogue of Pantoja's algorithm, in which the only independent variables are the components of a costate vector corresponding to the initial timestep. This reformulated algorithm gives exactly the Newton step for the initial costate with respect to a terminal transversality condition: at each timestep we solve implicit equations for the current controlsand successor costates. A remarkable feature of the indirect algorithm is that it is straiehtforward to comensate for the effect of non-zero residuals in the implicit costate equations. .The indirect reformulation of Pantoja's algorithm set out in this paper is a suitable basis for verified optimization using interval methods.

U2 - 10.1080/10556780108805833

DO - 10.1080/10556780108805833

M3 - Article

VL - 16

SP - 131

EP - 149

JO - Optimization Methods and Software

JF - Optimization Methods and Software

SN - 1055-6788

IS - 1-4

ER -