Numerical Methods for Optimal Control Problems with State Constraints
Pytlak, Radosław.
Numerical Methods for Optimal Control Problems with State Constraints [electronic resource] / by Radosław Pytlak. - XV, 218 p. online resource. - Lecture Notes in Mathematics, 1707 0075-8434 ; . - Lecture Notes in Mathematics, 1707 .
Estimates on solutions to differential equations and their approximations -- First order method -- Implementation -- Second order method -- Runge-Kutta based procedure for optimal control of differential— Algebraic Equations.
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.
9783540486626
10.1007/BFb0097244 doi
Systems theory.
Mathematical optimization.
Numerical analysis.
Economic theory.
Systems Theory, Control.
Calculus of Variations and Optimal Control; Optimization.
Numerical Analysis.
Economic Theory/Quantitative Economics/Mathematical Methods.
Q295 QA402.3-402.37
519
Numerical Methods for Optimal Control Problems with State Constraints [electronic resource] / by Radosław Pytlak. - XV, 218 p. online resource. - Lecture Notes in Mathematics, 1707 0075-8434 ; . - Lecture Notes in Mathematics, 1707 .
Estimates on solutions to differential equations and their approximations -- First order method -- Implementation -- Second order method -- Runge-Kutta based procedure for optimal control of differential— Algebraic Equations.
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.
9783540486626
10.1007/BFb0097244 doi
Systems theory.
Mathematical optimization.
Numerical analysis.
Economic theory.
Systems Theory, Control.
Calculus of Variations and Optimal Control; Optimization.
Numerical Analysis.
Economic Theory/Quantitative Economics/Mathematical Methods.
Q295 QA402.3-402.37
519