A numerical method for an optimal control problem with minimum sensitivity on coefficient variation

In this paper, we consider a class of optimal control problem involving an impulsive systems in which some of its coefficients are subject to variation. We formulate this optimal control problem as a two-stage optimal control problem. We first formulate the optimal impulsive control problem with all...

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Vydáno v:Applied mathematics and computation Ročník 218; číslo 4; s. 1180 - 1190
Hlavní autoři: Wei, W., Teo, K.L., Zhan, Z.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 15.10.2011
Témata:
Coefficient of variation
Coefficient variation
Computation
Computational algorithm
Computer programs
Impulsive system
Mathematical models
Optimal control
Optimization
Parametrization
Sensitivity analysis
Software packages
Computational algorithm
Sensitivity analysis
Coefficient variation
Optimal control
Impulsive system
ISSN:0096-3003, 1873-5649
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Shrnutí:In this paper, we consider a class of optimal control problem involving an impulsive systems in which some of its coefficients are subject to variation. We formulate this optimal control problem as a two-stage optimal control problem. We first formulate the optimal impulsive control problem with all its coefficients assigned to their nominal values. This becomes a standard optimal impulsive control problem and it can be solved by many existing optimal control computational techniques, such as the control parameterizations technique used in conjunction with the time scaling transform. The optimal control software package, MISER 3.3, is applicable. Then, we formulate the second optimal impulsive control problem, where the sensitivity of the variation of coefficients is minimized subject to an additional constraint indicating the allowable reduction in the optimal cost. The gradient formulae of the cost functional for the second optimal control problem are obtained. On this basis, a gradient-based computational method is established, and the optimal control software, MISER 3.3, can be applied. For illustration, two numerical examples are solved by using the proposed method.
Bibliografie:ObjectType-Article-1
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.05.093