本文讨论自反 Banach 空间 X 中点控制分布参数系统:(d/dt)x(t)=Ax(f)+u(t)f,0<t≤τ,x(0)=0,u(·)∈L^p(0,r)(1<P<∞),f∈D(A~*)′,x(τ;u)∈X的范数最优控制问题,算子 A 为 X 中强连续算子半群 T(t),t≥0的无穷小生成元,...本文讨论自反 Banach 空间 X 中点控制分布参数系统:(d/dt)x(t)=Ax(f)+u(t)f,0<t≤τ,x(0)=0,u(·)∈L^p(0,r)(1<P<∞),f∈D(A~*)′,x(τ;u)∈X的范数最优控制问题,算子 A 为 X 中强连续算子半群 T(t),t≥0的无穷小生成元,A~*是算子 A 的对偶算子,D(A~*)是 A~*的定义域,D(A~*)′是 D(A~*)的对偶子空间.利用 L^p(0,τ)空间的自反、光滑、严格凸性,用Banach 空间的对偶映射方法,证明了点控制系统的范数最优控制的存在唯一性,并给出了范数最优控制的形式表达式.展开更多
In this paper,we study the nonstationary population control systems:We regard the female-sum fertility rate β(t) as control auction ac judge its optimality by"norm minimum",and discuss the minimum norm cont...In this paper,we study the nonstationary population control systems:We regard the female-sum fertility rate β(t) as control auction ac judge its optimality by"norm minimum",and discuss the minimum norm control problems for the above population control systems.Utilizing space L2(0,T)’s reflexivity,smoothness and strict convexity,we prove the existence,the uniqueness and the approximation property of the minimum norm control for the nonstationary population control systems and give the corresponding optimality conditions by means of the methods of the dial mapping of Banach space.展开更多
文摘本文讨论自反 Banach 空间 X 中点控制分布参数系统:(d/dt)x(t)=Ax(f)+u(t)f,0<t≤τ,x(0)=0,u(·)∈L^p(0,r)(1<P<∞),f∈D(A~*)′,x(τ;u)∈X的范数最优控制问题,算子 A 为 X 中强连续算子半群 T(t),t≥0的无穷小生成元,A~*是算子 A 的对偶算子,D(A~*)是 A~*的定义域,D(A~*)′是 D(A~*)的对偶子空间.利用 L^p(0,τ)空间的自反、光滑、严格凸性,用Banach 空间的对偶映射方法,证明了点控制系统的范数最优控制的存在唯一性,并给出了范数最优控制的形式表达式.
文摘In this paper,we study the nonstationary population control systems:We regard the female-sum fertility rate β(t) as control auction ac judge its optimality by"norm minimum",and discuss the minimum norm control problems for the above population control systems.Utilizing space L2(0,T)’s reflexivity,smoothness and strict convexity,we prove the existence,the uniqueness and the approximation property of the minimum norm control for the nonstationary population control systems and give the corresponding optimality conditions by means of the methods of the dial mapping of Banach space.
