Redundancy allocation problem in dynamics systems using Pontryagin’s maximum principle Hamiltonian approach.

Abstract

This paper presents a dynamic optimal control framework for the Redundancy Allocation Problem (RAP) in multi-state systems with Binary-State Continuous Performance Level (BS-CPL) Components. While existing approaches, particularly those of Sharifi & Taghipour (2024), employ metaheuristic optimization techniques for static redundancy allocation, the present work introduces a time-dependent maintenance effort control based on Pontryagin’s Maximum Principle. Also the work applies Pontryagin’s Maximum Principle (PMP) to solve the Hamiltonian equation that captures system availability, degradation costs, reliability penalties, integer control constraints, and energy costs. The modified availability is integrated over the mission horizon to maximize total uptime. State dynamics follow Weibull degradation, costate equations enforce optimality and the optimal control law adapts redundancy in real time.The PMP-based approach is probably optimal, dynamically adaptive, and better suited for cost-sensitive, time-varying systems. Results are validated against analytical Weibull decay and PMP boundary conditions.