受控非线性系统在状态约束扰动下解的稳定性
Stability of solutions for controlled nonlinear systems under perturbation of state constraints
摘要：
研究了一类具有次线性增长但无界控制的非线性系统在时变状态约束摄动下的控制问题。它示出，给定的轨迹被近似，可以找到一个相邻的一个，位于内部的约束，并且可以任意接近的参考轨迹都在$L^\infty$ -距离和$L^2$ -控制成本。这一结果是证明基于内部解的状态约束逼近格式收敛性的重要工具，并适用于控制仿射系统。
英文摘要：
This paper tackles the problem of nonlinear systems, with sublinear growth but unbounded control, under perturbation of some time-varying state constraints. It is shown that, given a trajectory to be approximated, one can find a neighboring one that lies in the interior of the constraints, and which can be made arbitrarily close to the reference trajectory both in $L^\infty$-distance and $L^2$-control cost. This result is an important tool to prove the convergence of approximation schemes of state constraints based on interior solutions and is applicable to control-affine systems.
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