Numerical Methods for Optimal Control Problems with State Constraints

Radosław Pytlak (auth.)3540662146, 9783540662143

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.

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Table of contents :
Introduction….Pages 1-12
Estimates on solutions to differential equations and their approximations….Pages 13-26
First order method….Pages 27-53
Implementation….Pages 55-79
Second order method….Pages 81-128
Runge-Kutta based procedure for optimal control of differential— Algebraic Equations….Pages 129-168