论文标题
控制问题具有高阶的差异限制
Control problems with differential constraints of higher order
论文作者
论文摘要
我们认为成本最小化控制问题，其中动态系统受Euler-Lagrange类型的高阶微分方程的约束。遵循第一作者和第三作者的前几篇论文的想法，我们证明了控制$ u_o（t）$的曲线和一组初始条件$σ_O$ $ $ $为所考虑类型的控制问题提供了最佳解决方案，并且仅当适当的双积分大于或沿任何同质$（u（t，s），=（u（t，s））$ u _（u（s））$ u _（s）$ u _ cur cur cur cur cur cur y（u（t，s）） 0）$和$σ_O=σ（0）$。该属性称为“最小劳动原则”。根据这一原则，我们得出了经典的Pontryagin最大原理的概括，该原理在Euler-Lagrange类型的高阶差异约束下，而没有固定初始数据的假设。
We consider cost minimising control problems, in which the dynamical system is constrained by higher order differential equations of Euler-Lagrange type. Following ideas from a previous paper by the first and the third author, we prove that a curve of controls $u_o(t)$ and a set of initial conditions $σ_o$ gives an optimal solution for a control problem of the considered type if and only if an appropriate double integral is greater than or equal to zero along any homotopy $(u(t, s), σ(s))$ of control curves and initial data starting from $u_o(t) = u(t, 0)$ and $σ_o = σ(0)$. This property is called "Principle of Minimal Labour". From this principle we derive a generalisation of the classical Pontryagin Maximum Principle that holds under higher order differential constraints of Euler-Lagrange type and without the hypothesis of fixed initial data.
