Numerical Methods for Optimal Control Problems with State Constraints
Edition: 1 edition
Publisher: Springer
Published: September 29, 1999
Language: eng
Format: Paperback
Number of pages: 215
ISBN-13: 9783540662143
Subjects: Calculus of variations; Differential equations; Technology & Industrial Arts; Mathematics; General; Science/Mathematics; Robotics; Numerical Analysis; Linear Programming; Mathematics / Applied; Mathematics-Linear Programming; Medical-General; Necessary Optimality Conditions; Nonlinear Programming; Numerical Algorithms; Optimal Control; Control Theory; Advanced; Probability & Statistics - General; Mathematical optimization
Description: 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.
Notes: Lecture Notes in Mathematics