论文标题
开关和约束线性系统的数据驱动的稳定
Data-driven stabilization of switched and constrained linear systems
论文作者
论文摘要
我们考虑了过去嘈杂的输入状态轨迹测量值的开关信号和未知开关线性系统的连续输入的状态反馈控制定律的设计。基于Lyapunov-Metzler的不等式，我们得出了数据依赖数据的双线性程序，其解决方案直接返回可证明的稳定控制器，并确保$ \ Mathcal {H} _2 $或$ \ Mathcal {H} _ {\ infty} $ performance。我们进一步提出了大大降低计算成本的放松，但仍不需要任何开关模式的稳定性。最后，我们展示了方法对扰动线性系统的约束稳定问题的灵活性。我们通过数值来验证理论发现，证明了拟议的放松实现的保守主义与障碍性之间的良好权衡。
We consider the design of state feedback control laws for both the switching signal and the continuous input of an unknown switched linear system, given past noisy input-state trajectories measurements. Based on Lyapunov-Metzler inequalities, we derive data-dependent bilinear programs whose solution directly returns a provably stabilizing controller and ensures $\mathcal{H}_2$ or $\mathcal{H}_{\infty}$ performance. We further present relaxations that considerably reduce the computational cost, still without requiring stabilizability of any of the switching modes. Finally, we showcase the flexibility of our approach on the constrained stabilization problem for a perturbed linear system. We validate our theoretical findings numerically, demonstrating the favourable trade-off between conservatism and tractability achieved by the proposed relaxations.
