Adaptive control based on multiple sub-models and auxiliary variables for non-uniformly sampled data systems

For the control of non-uniformly sampled systems (NUSS), a new adaptive control method based on sub-models and auxiliary variables is proposed. First of all, the lifted state space model for a class of multi-rates systems non-uniformly sampled from their continuous-time systems are derived, and the corresponding discrete transfer function model is acquired by using mathematical theory derivation to analyze the state space model of NUSS. An auxiliary variables based identification algorithm is employed to confirm the discrete transfer function model by using the non-uniformly sampled data. The model of NUSS acquired from the identification algorithm is decomposed into the sub-models in accordance to optimization control principle. On this basis, the adaptive control method is obtained by designing the adaptive controller of each sub-model based on auxiliary variables. The parameter estimated-based adaptive control algorithm can virtually achieve optimal control and ensure that the closed-loop system is stable and globally convergent. Finally, the simulation example is studied to demonstrate the effectiveness of the proposed method.