This paper investigates the problem of inferring knowledge from data so that the inferred knowledge is interpretable and informative to humans who have prior knowledge. Given a dataset as a collection of system trajectories, we infer parametric linear temporal logic (pLTL) formulas that are informative and satisfied by the trajectories in the dataset with high probability. The informativeness of the inferred formula is measured by the information gain with respect to given prior knowledge represented by a prior probability distribution. We first present two algorithms to compute the information gain with a focus on two types of prior probability distributions: stationary probability distributions and probability distributions expressed by discrete time Markov chains. Then we provide a method to solve the inference problem for a subset of pLTL formulas with polynomial time complexity with respect to the number of Boolean connectives in the formula. We provide implementations of the proposed approach on explaining anomalous patterns, patterns changes and explaining the policies of Markov decision processes.
This paper focuses on developing a strategy for control of systems whose dynamics are almost entirely unknown.This situation arises naturally in a scenario where a system undergoes a critical failure. In that case, it is imperative to retain the ability to satisfy basic control objectives in order to avert an imminent catastrophe. A prime example of such an objective is the reach-avoid problem, where a system needs to move to a certain state in a constrained state space. To deal with limitations on our knowledge of system dynamics, we develop a theory of myopic control.The primary goal of myopic control is to, at any given time, optimize the current direction of the system trajectory, given solely the information obtained about the system until that time. We propose an algorithm that uses small perturbations in the control effort to learn local dynamics while simultaneously ensuring that the system moves in a direction that appears to be nearly optimal, and provide hard bounds for its suboptimality. We additionally verify the usefulness of the algorithm on a simulation of a damaged aircraft seeking to avoid a crash, as well as on an example of a Van der Pol oscillator.
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.
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