论文标题
有限维度LQ控制问题的汉密尔顿 - 雅各比 - 贝尔曼方程的收费公路属性和长期行为
The turnpike property and the long-time behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems
论文作者
论文摘要
我们分析了所谓的收费公路属性对对应于有限维线性季度最佳控制问题的价值函数的长时间行为的后果，并具有一般的终端成本和受约束的控制。 我们证明，当Time Horizon $ T $倾向于无穷大时，该值函数的行为为$ W（X） + C \，T +λ$，并且我们提供了这三个术语中每个术语的控制解释，从而与Thrpike属性清楚了链接。 作为副产品，我们获得了相关的汉密尔顿 - 雅各比 - 贝尔曼方程的解决方案的长期行为，而在动量变量中，哈密顿人不强制性。由于独立兴趣，我们表明线性季度最佳控制问题受约束控制属性属性，尤其是当稳定的最佳最佳可能使控制约束饱和时。
We analyze the consequences that the so-called turnpike property has on the long-time behavior of the value function corresponding to a finite-dimensional linear-quadratic optimal control problem with general terminal cost and constrained controls. We prove that, when the time horizon $T$ tends to infinity, the value function asymptotically behaves as $W(x) + c\, T + λ$, and we provide a control interpretation of each of these three terms, making clear the link with the turnpike property. As a by-product, we obtain the long-time behavior of the solution to the associated Hamilton-Jacobi-Bellman equation in a case where the Hamiltonian is not coercive in the momentum variable. As a result of independent interest, we showed that linear-quadratic optimal control problems with constrained control enjoy a turnpike property, also particularly when the steady optimum may saturate the control constraints.
