控制资源有限的控制系统可积轨线的鲁棒性
On the Robustness of the Integrable Trajectories of the Control Systems with Limited Control Resources
摘要：
研究了由Urysohn型积分方程描述的控制系统，其中系统关于相矢量是非线性的，关于控制矢量是仿射的。控制函数从半径为$r$且以原点为中心的空间$L_q\left(Ω;\mathbb{R}^m\right),$ $q>1,$的闭合球中选择。系统的轨迹被定义为来自空间$L_p\left(Ω;\mathbb{R}^n\right),$ $\frac{1}{q}+\frac{1}{p}=1,$的$p$ -可积多变量函数，该函数几乎处处满足系统方程。结果表明，系统的轨迹是鲁棒的剩余控制资源。应用这一结果，证明了每一条轨迹都可以用完全消耗总控制资源所得到的轨迹来近似。
英文摘要：
The control system described by Urysohn type integral equation is considered where the system is nonlinear with respect to the phase vector and is affine with respect to the control vector. The control functions are chosen from the closed ball of the space $L_q\left(Ω;\mathbb{R}^m\right),$ $q>1,$ with radius $r$ and centered at the origin. The trajectory of the system is defined as $p$-integrable multivariable function from the space $L_p\left(Ω;\mathbb{R}^n\right),$ $\frac{1}{q}+\frac{1}{p}=1,$ satisfying the system's equation almost everywhere. It is shown that the system's trajectories are robust with respect to the remaining control resource. Applying this result it is proved that every trajectory can be approximated by the trajectory obtained by full consumption of the total control resource.
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