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Worst case analysis of nonlinear systems

机译：非线性系统的最坏情况分析

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摘要

The authors work out a framework for evaluating the performance of a continuous-time nonlinear system when this is quantified as the maximal value at an output port under bounded disturbances-the disturbance problem. This is useful in computing gain functions and L ∞-induced norms, which are often used to characterize performance and robustness of feedback systems. The approach is variational and relies on the theory of viscosity solutions of Hamilton-Jacobi equations. Convergence of Euler approximation schemes via discrete dynamic programming is established. The authors also provide an algorithm to compute upper bounds for value functions. Differences between the disturbance problem and the optimal control problem are noted, and a proof of convergence of approximation schemes for the control problem is given. Case studies are presented which assess the robustness of a feedback system and the quality of trajectory tracking in the presence of structured uncertainty
机译：作者设计了一个框架，用于评估连续时间非线性系统的性能，当该时间被量化为有界干扰（干扰问题）下输出端口的最大值时。这在计算增益函数和L∞诱导的范数时很有用，这些函数通常用于表征反馈系统的性能和鲁棒性。该方法是可变的，并依赖于Hamilton-Jacobi方程的粘度解理论。建立了通过离散动态规划的欧拉逼近方案的收敛性。作者还提供了一种算法来计算值函数的上限。指出了扰动问题和最优控制问题之间的差异，并给出了控制问题的近似方案的收敛性证明。提出了案例研究，评估了存在结构不确定性时反馈系统的鲁棒性和轨迹跟踪的质量

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