耗散系统有限到无限时域最优控制问题中的模式保持
Pattern preservation in finite to infinite-horizon optimal control problems for dissipative systems
AI总结：
研究耗散系统无限时域最优控制问题及其与有限时域公式的关系，通过存在强制存储函数时状态方程的耗散性，证明无限时域最优控制可由有限时域极限得到，建立相关理论联系并给出数值示例。
摘要：
本文聚焦于耗散系统的无限时域最优控制问题及其与有限时域公式的关系。我们表明，对于一大类问题，当存在强制存储函数时，状态方程的耗散性意味着无限时域最优控制可以作为相应有限时域最优控制的极限得到。此属性称为模式保持或模式保持属性。我们的分析在最优控制中建立了耗散理论与变分收敛框架之间的形式联系，从而为验证模式保持提供了一个具体且数值上易于处理的条件。数值示例说明了所提出充分条件的有效性和局限性。
英文摘要：
This paper focuses on infinite-horizon optimal control problems for dissipative systems and the relations to their finite-horizon formulations. We show that, for a large class of problems, dissipativity of the state equation, when a coercive storage function exists, implies that infinite-horizon optimal controls can be obtained as limits of the corresponding finite-horizon ones. This property is referred to as pattern preservation, or pattern-preserving property. Our analysis establishes a formal link between dissipativity theory and the variational convergence framework in optimal control, thus providing a concrete and numerically tractable condition for verifying pattern preservation. Numerical examples illustrate the effectiveness and limitations of the proposed sufficient conditions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
