通过高效求解最小-最大优化问题实现非线性系统的鲁棒输出反馈
Robust Output Feedback of Nonlinear Systems through the Efficient Solution of Min-Max Optimization Problems
AI总结：
针对带界不确定离散非线性系统的鲁棒输出反馈控制，提出构建半无限规划的方法，无需显式状态估计即可保证性能，结合局部约简技术加速求解，在二维四旋翼测试中实现了鲁棒约束满足与跟踪。
摘要：
我们研究了受动力学和测量环节有界不确定性影响的离散时间非线性系统的鲁棒输出反馈控制问题。具体而言，我们展示了如何构建半无限规划（semi-infinite programs），以生成在有限预测时域内、针对系统不确定性最坏情况实现下最小化某一期望性能代价的增益，同时确保所有指定的非线性约束始终得到满足。求解过程依赖于通过历史测量值和系统动力学对可行状态空间的隐式描述，并假设系统始终处于可行空间中对性能最不利的子集内。通过这种方式，我们无需借助任何显式状态估计，即可保证系统的真实状态满足所有选定的性能准则。在若干平滑性假设下，我们还讨论了通过局部约简技术求解这些半无限规划的方法，该技术会为不确定性实现生成最优场景集，以近似连续不确定性空间并加快最优解的计算速度。在二维非线性四旋翼（quadrotor）上进行测试时，所提出的方法即便在处理高度不确定的测量值和系统动力学的情况下，仍能实现鲁棒的约束满足和跟踪效果。
英文摘要：
We examine robust output feedback control of discrete-time nonlinear systems with bounded uncertainties affecting the dynamics and measurements. Specifically, we demonstrate how to construct semi-infinite programs that produce gains to minimize some desired performance cost over a finite prediction horizon for the worst-case realization of the system's uncertainties, while also ensuring that any specified nonlinear constraints are always satisfied. The solution process relies on an implicit description of the feasible state space through prior measurements and the system dynamics, and assumes that the system is always in the subset of the feasible space that is most detrimental to performance. In doing so, we can guarantee that the system's true state will meet all of the chosen performance criteria without resorting to any explicit state estimation. Under some smoothness assumptions, we also discuss solving these semi-infinite programs through local reduction techniques, which generate optimal scenario sets for the uncertainty realizations to approximate the continuous uncertainty space and speed up the computation of optima. When tested on a two-dimensional nonlinear quadrotor, the developed method achieves robust constraint satisfaction and tracking despite dealing with highly uncertain measurements and system dynamics.
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