Affiliations: [a] Department of Computer and Information Science, Indiana University Purdue University Indianapolis, 723 W Michigan St SL 280 Indianapolis, Indiana 46202, United States. E-mails: thamnguy@iupui.edu, smukhopa@iupui.edu | [b] Department of Water Resources Engineering, Oregon State University, 1691 SW Campus Way, Owen Hall 211, Corvallis, Oregon, 97331, United States. E-mail: meghna@oregonstate.edu
Abstract: Multidisciplinary Design Optimization (MDO) is a computational approach for optimizing design of a complex system of systems that require knowledge from multiple disciplines. In a former study, we explored and found that the individual discipline feasible (IDF), a type of MDO design technique, performed well in several benchmark test cases of decentralized Reinforcement Learning (RL) problems, in particular, stabilizing an unknown system. However, the earlier study was not able to resolve as to why the overall system of systems, even with strongly coupled systems, could be stabilized when each agent just focused on stabilizing itself. In this work, we make significant extension in resolving this behavior by conducting a theoretical analysis of the MDO solution of RL problems. Through the analysis, we show that with the proper control law, each MDO agent should be able to bring its state closer to the 0-stable point regardless of how the other agents’ states impact the state of the whole system. This is the main reason why the ‘selfish’ MDO-IDF agents are successful in learning to stabilize the overall system. The simulation results, including benchmark test cases, verify our analysis. Therefore, we propose that the MDO would be a promising solution in many other decentralized RL problems.
