Dynamic Certainty Equivalence Adaptive Control by Nonlinear Parameter Filtering

This paper presents a novel solution to the problem of designing an implementable (i.e., differentiator-free) model-reference output-feedback direct-adaptive controller for single-input-single-output linear time-invariant systems with relative degree possibly larger than one. The new paradigm is based on a version of the Dynamic Certainty Equivalence (DyCE) principle. The approach proposed in this work consists in realizing the DyCE control through surrogate parameter derivatives, made available by a Nonlinear Parameter Filter (NPF), instead of feeding the DyCE controller with the derivatives of the estimates produced High-Order Tuner (HOT). The proposed adaptive controller does not require error augmentation or normalization, allowing the use of large adaptation gains for fast convergence speed. Moreover, the proposed architecture can be easily equipped with well-known robust modifications of tuning laws. The performance of the proposed algorithm is demonstrated via comparative simulations with an error augmentation-based method and a simplified HOT algorithm.