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AuthorPytlak, Radosล{130}aw. author
TitleNumerical Methods for Optimal Control Problems with State Constraints [electronic resource] / by Radosล{130}aw Pytlak
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1999
Connect tohttp://dx.doi.org/10.1007/BFb0097244
Descript XV, 218 p. online resource

SUMMARY

While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new methods. Among others, a novel convergence analysis of optimal control algorithms is introduced. The analysis refers to the topology of relaxed controls only to a limited degree and makes little use of Lagrange multipliers corresponding to state constraints. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods. Further, the implementation aspects of the methods developed in the book are presented and discussed. The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature


CONTENT

Estimates on solutions to differential equations and their approximations -- First order method -- Implementation -- Second order method -- Runge-Kutta based procedure for optimal control of differentialโ{128}{148} Algebraic Equations


Mathematics System theory Numerical analysis Calculus of variations Economic theory Mathematics Systems Theory Control Calculus of Variations and Optimal Control; Optimization Numerical Analysis Economic Theory/Quantitative Economics/Mathematical Methods



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