Sensor activation policy optimization for K-diagnosability based on multi-agent reinforcement learning

Ensuring K-diagnosability in partially observable discrete-event systems is vital for maintaining safe and reliable system operation. In practical settings where full sensor deployment is prohibitively expensive or physically constrained, optimizing sensor usage becomes essential. This study addresses the sensor activation optimization problem for K-diagnosability using multi-agent reinforcement learning. A compact most permissive observer with reduced construction burden is introduced, which embeds all admissible sensor activation policies ensuring K-diagnosability. The optimization problem is then formulated as a Markov game with a maximum discounted total cost objective, allowing for quantitative evaluation of each sensor activation policy. To solve this game-theoretic problem, a minimax Q-learning algorithm is employed, enabling agents to collaboratively learn robust sensor activation policies under adversarial dynamics. The effectiveness and practical relevance of the proposed method are demonstrated through four illustrative examples and two case studies. Experimental results confirm that the proposed method identifies cost-efficient sensor activation policies that preserve K-diagnosability across both finite-cost and infinite-cost scenarios. Beyond fault diagnosis, the proposed method lays the foundation for solving broader optimization problems, such as opacity enforcement and privacy protection, thereby offering a unified and flexible solution for intelligent sensor management in cyber-physical systems.