Reinforcement Learning-Based Membership Function Optimization and Non-Fragile Control for IT2 Polynomial Fuzzy Switched Positive Systems

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Abstract
This paper proposes a reinforcement learning-based membership function optimization and embedding (RL-MFOE) control scheme for interval type-2 (IT2) polynomial fuzzy switched positive systems. A non-fragile static output feedback controller is designed to handle parameter uncertainties and external disturbances, guaranteeing a prescribed L1-gain performance. A matrix factorization technique is introduced to resolve the non-convex coupling between unknown positive vectors and controller gains. In the proposed scheme, a reinforcement learning algorithm tunes the parameters of the IT2 fuzzy membership functions (MFs) in a data-driven manner, where the decay rate serves as the reward signal guiding the optimization. The optimized MFs are expressed in polynomial form and incorporated into sum-of-squares (SOS) stability conditions via relaxation matrices, which reduces the conservatism in stability analysis, facilitates higher decay rates, and in turn allows stricter mode-dependent average dwell time (MDADT) bounds. By iteratively updating the MF parameters, the scheme satisfies the prescribed L1-gain performance and supports higher switching frequencies while preserving system positivity and stability. Two simulation examples validate the effectiveness of the proposed methodology.
Funding Information
  • Science and Technology Department of Tibet Autonomous Region (QN2025118)
  • Natural Science Foundation (62503412)
  • Science and Technology Department of Ningxia Province (202301A295)

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