Numerical Methods for Optimal Control Problems with State Constraints

1. Front Matter

   Pages I-XIV

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2. Introduction

   • Radosław Pytlak

   Pages 1-12

3. Estimates on solutions to differential equations and their approximations

   • Radosław Pytlak

   Pages 13-26

4. First order method

   • Radosław Pytlak

   Pages 27-53

5. Implementation

   • Radosław Pytlak

   Pages 55-79

6. Second order method

   • Radosław Pytlak

   Pages 81-128

7. Runge-Kutta based procedure for optimal control of differential — Algebraic Equations

   • Radosław Pytlak

   Pages 129-168

8. Back Matter

   Pages 169-216

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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.

• Necessary Optimality Conditions
• Nonlinear Programming
• Numerical Algorithms
• Optimal control
• Optimality Conditions
• State Constrained Problems
• algorithms
• ordinary differential equation

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