An optimal self-healing policy with discrete resources

Abstract

Intelligent systems capable of detecting and repairing damage autonomously hold significant promise across various domains, such as space exploration, autonomous vehicles, and robotics. Integrating self-healing mechanisms is pivotal in enhancing these systems’ durability, reliability, and efficiency. This paper introduces a novel self-healing policy with discrete self-healing resources. Self-inspections at equidistant time epochs reveal the deterioration of the system. Various actions, including doing nothing, self-healing, and stopping, can be selected after inspection. A self-healing action reduces deterioration to a random lower level, with the degree of reduction depending on the amount of healing resources used. Therefore, it is crucial to determine the optimal number of healing resources to allocate during self-healing. The goal is to identify the policy that minimizes the expected average cost. This optimization problem is formulated within the semi-Markov decision process framework. The structural properties of the optimal policy are examined. A policy iteration algorithm is developed based on a discretization approach. A numerical example is used to show how to apply the proposed approach, and the obtained policy provides valuable insights to support the operation of intelligent systems.