论文标题
在连续无限的地平线上，最佳控制 - 消散性，稳定性和横向性
On Continuous-Time Infinite Horizon Optimal Control -- Dissipativity, Stability and Transversality
论文作者
论文摘要
本文分析了连续时间无限 - 马最佳控制问题（OCP）中消散性和稳定性之间的相互作用。我们在这些属性之间建立了几种关系，这些关系在一组等效条件下达到顶峰。此外，我们研究了无限 - 水 - 最佳伴随轨迹的收敛性和稳定性。我们的调查的主力是OCP中严格散发性的概念，这是在经济模型预测控制的背景下创造的。关于稳定性与耗散性之间的联系，本文可以将其视为最小二乘在1971年以来最小二乘最佳控制的开创性工作的扩展。此外，我们表明，严格的耗散性为无限范围内的稳定状态跨越了1974年以不同的条件的稳定，对邻近性的邻近条件的最佳问题提供了一个最佳的答案。 价值。我们借鉴了几个例子来说明我们的发现。此外，我们讨论了我们的发现与文献中可用的结果的关系。
This paper analyses the interplay between dissipativity and stability properties in continuous-time infinite-horizon Optimal Control Problems (OCPs). We establish several relations between these properties, which culminate in a set of equivalence conditions. Moreover, we investigate convergence and stability of the infinite-horizon optimal adjoint trajectories. The workhorse for our investigations is a notion of strict dissipativity in OCPs, which has been coined in the context of economic model predictive control. With respect to the link between stability and dissipativity, the present paper can be seen as an extension of the seminal work on least squares optimal control by Willems from 1971. Furthermore, we show that strict dissipativity provides a conclusive answer to the question of adjoint transversality conditions in infinite-horizon optimal control which has been raised by Halkin in 1974. Put differently, we establish conditions under which the adjoints converge to their optimal steady state value. We draw upon several examples to illustrate our findings. Moreover, we discuss the relation of our findings to results available in the literature.
