Asymptotic controllability and optimal control

详细信息    查看全文

• 作者：M. Motta ^{motta@math.unipd.it} ; F. Rampazzo ; ^{rampazzo@math.unipd.it}
• 关键词：49J15 ; 93D05
• 刊名：Journal of Differential Equations
• 出版年：2013
• 出版时间：1 April, 2013
• 年：2013
• 卷：254
• 期：7
• 页码：2744-2763
• 全文大小：350 K

文摘

We consider a control problem where the state must approach asymptotically a target C while paying an integral cost with a non-negative Lagrangian l. The dynamics f is just continuous, and no assumptions are made on the zero level set of the Lagrangian l. Through an inequality involving a positive number and a Minimum Restraint Function - a special type of Control Lyapunov Function - we provide a condition implying that (i) the system is asymptotically controllable, and (ii) the value function is bounded by . The result has significant consequences for the uniqueness issue of the corresponding Hamilton-Jacobi equation. Furthermore it may be regarded as a first step in the direction of a feedback construction.