Optimizing adaptive loading and abort decisions considering state-dependent reward

In safety-critical systems, failure mechanisms are fundamentally governed by operational loads, presenting opportunities for risk mitigation via dynamic load management. Additionally, mission aborts serve as an effective measure to enhance system safety during mission operations. This research examines systems executing successive missions with variable workloads, aiming to optimize the balance between mission success probability and system survivability through decisions on abort timing and load levels. We focus on two key decision processes: determining the optimal timing for mission aborts and selecting appropriate load levels prior to mission termination. The goal is to maximize expected revenue, considering mission completion rewards, mission failure costs, and system failure costs, through strategic load and abort policies. Framed within a Markov decision process, we establish sufficient conditions for the value functions to be monotonic and convex. Additionally, we identify conditions that ensure monotonicity in loading policies and facilitate simplified decision rules. Case studies involving temperature control systems in chemical reactors illustrate the practical relevance of our theoretical results.