Proceedings of the SIAM Conference on Control and Its Applications. SIAM Conference on Control and Its Applications最新文献

英文中文

Online Inner Approximation of Reachable Sets of Nonlinear Systems with Diminished Control Authority. 控制权限减小非线性系统可达集的在线内逼近。

Proceedings of the SIAM Conference on Control and Its Applications. SIAM Conference on Control and Its Applications

Pub Date : 2021-01-01 DOI: 10.1137/1.9781611976847.2

Hamza El-Kebir, Melkior Ornik

This work presents a method of efficiently computing inner approximations of forward reachable sets for nonlinear control systems with diminished control authority, given an a priori computed reachable set for the nominal system. The method functions by shrinking a precomputed convex reachable set based on a priori knowledge of the system's trajectory deviation growth dynamics. The trajectory deviation growth dynamics determine an upper bound on the minimal deviation between two trajectories emanating from the same point that are generated by control inputs from the nominal and diminished set of control inputs, respectively. These growth dynamics are a function of a given Hausdorff distance bound between the nominal convex space of admissible controls and the possibly unknown impaired space of admissible controls. Because of its relative computational efficiency compared to direct computation of the off-nominal reachable set, this procedure can be applied to onboard fault-tolerant path planning and failure recovery. We consider the implementation of the approximation procedure by way of numerical integration and a root finding scheme, and we present two illustrative examples, namely an application to a control system with quadratic nonlinearities and aircraft wing rock dynamics.

本文提出了一种有效计算控制权限减小非线性控制系统前向可达集内逼近的方法，给出了标称系统的先验计算可达集。该方法基于系统轨迹偏差增长动力学的先验知识，通过收缩预先计算的凸可达集来实现。轨迹偏差增长动力学决定了从同一点发出的两条轨迹之间最小偏差的上限，这两条轨迹分别由标称控制输入和减少控制输入产生。这些增长动力学是允许控制的名义凸空间和可能未知的允许控制的受损空间之间给定的Hausdorff距离的函数。与直接计算非标称可达集相比，该方法具有相对的计算效率，可以应用于机载容错路径规划和故障恢复。我们考虑用数值积分和寻根格式来实现逼近过程，并给出了两个示例，即二次非线性控制系统和飞机机翼岩石动力学的应用。

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引用次数: 4

Quantitative Resilience of Linear Driftless Systems. 线性无漂移系统的定量复原力。

Proceedings of the SIAM Conference on Control and Its Applications. SIAM Conference on Control and Its Applications

Pub Date : 2021-01-01 DOI: 10.1137/1.9781611976847.5

Jean-Baptiste Bouvier, Kathleen Xu, Melkior Ornik

This paper introduces the notion of quantitative resilience of a control system. Following prior work, we study linear driftless systems enduring a loss of control authority over some of their actuators. Such a malfunction results in actuators producing possibly undesirable inputs over which the controller has real-time readings but no control. By definition, a system is resilient if it can still reach a target after a partial loss of control authority. However, after a malfunction, a resilient system might be significantly slower to reach a target compared to its initial capabilities. We quantify this loss of performance through the new concept of quantitative resilience. We define such a metric as the maximal ratio of the minimal times required to reach any target for the initial and malfunctioning systems. Naïve computation of quantitative resilience directly from the definition is a complex task as it requires solving four nested, possibly nonlinear, optimization problems. The main technical contribution of this work is to provide an efficient method to compute quantitative resilience. Relying on control theory and on two novel geometric results we reduce the computation of quantitative resilience to a single linear optimization problem. We demonstrate our method on an opinion dynamics scenario.

本文介绍了控制系统定量复原力的概念。根据之前的工作，我们研究的是线性无漂移系统，该系统的某些执行器失去了控制权。这种故障会导致执行器产生可能不需要的输入，而控制器对这些输入有实时读数，但却无法控制。根据定义，如果系统在失去部分控制权后仍能达到目标，则该系统具有弹性。然而，在发生故障后，弹性系统达到目标的速度可能会大大低于其初始能力。我们通过定量复原力这一新概念来量化这种性能损失。我们将这一指标定义为初始系统和故障系统到达任何目标所需的最短时间的最大比值。根据定义直接计算定量弹性是一项复杂的任务，因为它需要解决四个嵌套的、可能是非线性的优化问题。这项工作的主要技术贡献在于提供了一种计算定量复原力的有效方法。依靠控制理论和两个新颖的几何结果，我们将定量弹性的计算简化为一个单一的线性优化问题。我们在一个舆情动态场景中演示了我们的方法。

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引用次数: 0

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