The focus of this paper is on the development of velocity constrained time-optimal control profiles for point-to-point motion of a gantry crane system. Assuming that the velocity of the trolley of the crane can be commanded, an optimal control problem is posed to determine the bang-off-bang control profile to transition the system to the terminal states with no residual vibrations. Both undamped and underdamped systems are considered and the variation of the structure of the optimal control profiles as a function of the final displacement is studied and the collapse and birthing of switches in the control profile are explained. To account for uncertainties in model parameters, a robust controller design is posed and the tradeoff of increase in maneuver time to the reduction of residual vibrations is illustrated.
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This content will become publicly available on December 1, 2024
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 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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- Award ID(s):
- 2031213
- NSF-PAR ID:
- 10481503
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Computational Optimization and Applications
- Volume:
- 86
- Issue:
- 3
- ISSN:
- 0926-6003
- Page Range / eLocation ID:
- 1229 to 1246
- Subject(s) / Keyword(s):
- Switch point algorithm Singular control Bang–bang control Boundary-value problems
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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