Extension of switch point algorithm to boundary-value problems

In an earlier paper ( https://doi.org/10.1137/21M1393315 ), the switch point algorithm was developed for solving optimal control problems whose solutions are either singular or bang-bang or both singular and bang-bang, and which possess a finite number of jump discontinuities in an optimal control a...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 86; no. 3; pp. 1229 - 1246
Main Author: Hager, William W.
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2023
Springer Nature B.V
Subjects:
Algorithms
Boundary value problems
Control theory
Convex and Discrete Geometry
Management Science
Mathematical analysis
Mathematics
Mathematics and Statistics
Operations Research
Operations Research/Decision Theory
Optimal control
Optimization
Statistics
Terminal constraints
Singular control
65K05
90C30
Boundary-value problems
Bang–bang control
49M37
49M25
Switch point algorithm
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary:In an earlier paper ( https://doi.org/10.1137/21M1393315 ), the switch point algorithm was developed for solving optimal control problems whose solutions are either singular or bang-bang or both singular and bang-bang, and which possess a finite number of jump discontinuities in an optimal control at the points in time where the solution structure changes. The class of control problems that were considered had a given initial condition, but no terminal constraint. The theory is now extended to include problems with both initial and terminal constraints, a structure that often arises in boundary-value problems. Substantial changes to the theory are needed to handle this more general setting. Nonetheless, the derivative of the cost with respect to a switch point is again the jump in the Hamiltonian at the switch point.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-023-00530-y