Related papers: A Necessary Condition on Chain Reachable Robustnes…

We argue that robustness of explanations---i.e., that similar inputs should give rise to similar explanations---is a key desideratum for interpretability. We introduce metrics to quantify robustness and demonstrate that current methods do…

The present article introduces a reference framework for discussing resilience of computational systems. Rather than a property that may or may not be exhibited by a system, resilience is interpreted here as the emerging result of a dynamic…

We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…

Hamilton Jacobi (HJ) Reachability is a formal verification tool widely used in robotic safety analysis. Given a target set as unsafe states, a dynamical system is guaranteed not to enter the target under the worst-case disturbance if it…

Robustness of a distributed computing system is defined as the ability to maintain its performance in the presence of uncertain parameters. Uncertainty is a key problem in heterogeneous (and even homogeneous) distributed computing systems…

In this note, we consider the problem of choosing which nodes of a linear dynamical system should be actuated so that the state transfer from the system's initial condition to a given final state is possible. Assuming a standard complexity…

Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…

Resilience is a rehashed concept in natural hazard management - resilience of cities to earthquakes, to floods, to fire, etc. In a word, a system is said to be resilient if there exists a strategy that can drive the system state back to…

Robustness is often regarded as a critical future challenge for real-world applications, where stability is essential. However, as models often learn tasks in a similar order, we hypothesize that easier tasks will be easier regardless of…

Non-conservative loads of the follower type are usually believed to be the source of dynamic instabilities such as flutter and divergence. It is shown that these instabilities (including Hopf bifurcation, flutter, divergence, and…

Uneven terrain necessarily transforms periodic walking into a non-periodic motion. As such, traditional stability analysis tools no longer adequately capture the ability of a bipedal robot to locomote in the presence of such disturbances.…

Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…

We introduce three measures which quantify the degree to which quantum systems possess the robustness exhibited by classical systems when subjected to continuous observation. Using these we show that for a fixed environmental interaction…

While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…

The consensus that complexity begets stability in ecosystems was challenged in the seventies, a result recently extended to ecologically-inspired networks. The approaches assume the existence of a feasible equilibrium, i.e. with positive…

Turing computability is the standard computability paradigm which captures the computational power of digital computers. To understand whether one can create physically realistic devices which have super-Turing power, one needs to…

We study the problem of robust performance of quantum systems under structured uncertainties. A specific feature of closed (Hamiltonian) quantum systems is that their poles lie on the imaginary axis and that neither a coherent controller…

The stability of solutions to evolution equations with respect to small stochastic perturbations is considered. The stability of a stochastic dynamical system is characterized by the local stability index. The limit of this index with…

We prove a robust converse barrier function theorem via the converse Lyapunov theory. While the use of a Lyapunov function as a barrier function is straightforward, the existence of a converse Lyapunov function as a barrier function for a…

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to…