Abstract
Due to the difficulties of handling non-linearities in many large systems to which on-line optimal control is being applied, many applications have had to be restricted to the linear model-quadratic cost case. In particular, if the calculations are performed in a decentralized manner, the sub-system problems must yield a rapid solution and in the simple linear-quadratic case analytic solutions to these sub-problems may be obtained. The method of quasilinearization for the resolution of boundary-value problems arising in the solution of non-linear differential equations has been widely developed. This paper examines the use of quasilinearization algorithms for the solution of sub-problems arising in a problem decomposition using Lagrangian duality. The good convergence properties of the algorithms make them particularly useful for the solution of the sub-system problems. The actual improvement in operating costs obtained by handling more general sub-system non-linearities is compared with the increased computational burden for an actual on-line water control scheme.
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Keywords
- Water Distribution Network
- Lagrangian Duality
- Decentralize Manner
- Quasilinearization Method
- Water Supply Problem
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References
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© 1976 Springer-Verlag
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Fallside, F., Perry, P.F. (1976). On the use of quasilinearization for the solution of sub-problems in on-line hierarchical control and its application to a water distribution network. In: Cea, J. (eds) Optimization Techniques Modeling and Optimization in the Service of Man Part 1. Optimization Techniques 1975. Lecture Notes in Computer Science, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07622-0_476
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DOI: https://doi.org/10.1007/3-540-07622-0_476
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