## Variational and Optimal Control Problems on Unbounded DomainsThis volume contains the proceedings of the workshop on Variational and Optimal Control Problems on Unbounded Domains, held in memory of Arie Leizarowitz, from January 9-12, 2012, in Haifa, Israel. The workshop brought together a select group of worldwide experts in optimal control theory and the calculus of variations, working on problems on unbounded domains. The papers in this volume cover many different areas of optimal control and its applications. Topics include needle variations in infinite-horizon optimal control, Lyapunov stability with some extensions, small noise large time asymptotics for the normalized Feynman-Kac semigroup, linear-quadratic optimal control problems with state delays, time-optimal control of wafer stage positioning, second order optimality conditions in optimal control, state and time transformations of infinite horizon problems, turnpike properties of dynamic zero-sum games, and an infinite-horizon variational problem on an infinite strip. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel). |

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### Contents

1 | |

Comments on Lyapunov stability with Some Extensions | 19 |

Small Noise Large Time Asymptotics for the Normalized FeynmanKac Semigroup | 31 |

Linear Constraints for Convex Approximation of the Stability Domain of a Polynomial in Coefficients Space | 49 |

Singular Solution of an Infinite Horizon LinearQuadratic Optimal Control Problem with State Delays | 59 |

TimeOptimal Control of Wafer Stage Positioning Using Simplified Models | 99 |

Robust Stability and Monitoring Threshold Functions | 109 |

One Dimensional Singular Calculus of Variations in Infinite Horizon and Applications | 131 |

Second Order Optimality Conditions in Optimal Control Problems with Mixed Inequality Type Constraints on a Variable Time Interval | 141 |

An InfiniteHorizon Variational Problem on an Infinite Strip | 157 |

State and Time Transformations of Infinite Horizon Optimal Control Problems | 189 |

Turnpike Properties of Approximate Solutions of DiscreteTime Optimal Control Problems on Compact Metric Spaces | 209 |

Turnpike Theory for Dynamic ZeroSum Games | 225 |