To design critical systems engineers must be able to prove that their system can continue with its mission even after losing control authority over some of its 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 such a malfunction, a resilient system might be significantly slower to reach a target compared to its initial capabilities. To quantify this loss of performance we introduce the notion of quantitative resilience as the maximal ratio of the minimal times required to reach any target for the initial and malfunctioning systems. Naive 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 of control systems with multiple integrators and nonsymmetric input sets. Relying on control theory and on two novel geometric results we reduce the computation of quantitative resilience to a linear optimization problem. We illustrate our method on two numerical examples – a trajectory controller for low-thrust spacecrafts and a UAV with eight propellers.

Motivated by the question of optimal facility placement, the classical p-dispersion problem seeks to place a fixed number of equally sized non-overlapping circles of maximal possible radius into a subset of the plane. While exact solutions to this problem may be found for placement into particular sets, the problem is provably NP-complete for general sets, and existing work is largely restricted to geometrically simple sets. This paper makes two contributions to the theory of p-dispersion. First, we propose a computationally feasible suboptimal approach to the p-dispersion problem for all non-convex polygons. The proposed method, motivated by the mechanics of the p-body problem, considers circle centers as continuously moving objects in the plane and assigns repulsive forces between different circles, as well as circles and polygon boundaries, with magnitudes inversely proportional to the corresponding distances. Additionally, following the motivating application of optimal facility placement, we consider existence of additional hard upper or lower distance bounds on pairs of circle centers, and adapt the proposed method to provide a p-dispersion solution that provably respects such constraints. We validate our proposed method by comparing it with previous exact and approximate methods for p-dispersion. The method quickly produces near-optimal results for a number of containers.

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 such 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.

Increasing interest in asteroid mining and in-situ resource utilization will lead to an increase in asteroid surface operations. The geophysical properties of asteroids are often unknown and play a significant role in the resulting gravitational fields. Surface operations such as mining may significantly alter the asteroid’s structure or, in the case of contact binary asteroids, cause the asteroid to split depending on the rotational condition. The coupled problem of estimating unknown parameters of a splitting contact-binary system and controlling a spacecraft’s trajectory in the system’s vicinity is investigated. An indirect adaptive control scheme is utilized to simultaneously meet both objectives. The results are compared with the traditional 2-body controller and the improvement enabled by the proposed scheme is demonstrated.