Weighted multiple model adaptive control with self-tuning model

The issues of model set construction and weighting algorithm analysis in multiple model adaptive control of discrete-time systems with large parameter uncertainty are considered in this paper. First, to improve system performance by reducing the calculation burden and relaxing the convergence conditions for the classical weighting algorithm, a new weighting algorithm is adopted, which is based on the model output errors of the multi-model adaptive control system with a self-tuning model. Second, the weighting algorithm convergence is analyzed in two cases:when the model set contains the true model of plant and it tends to the fixed model, and when the model set does not contain the true model of plant and it tends to the self-tuning model. Third, according to the virtual equivalent system (VES) concept and methodology, the stability of weighted multiple model adaptive control (WMMAC) with a self-tuning model is presented under a unified framework. The analysis procedures for linear time-invariant (LTI) and parameter jump plants are independent of specific local control methods and weighting algorithm, which only require that each local controller stabilizes the corresponding local model, the output of the formed closed-loop system tracks the reference signal, and the weighting algorithm is convergent. The principal contributions of the paper are the analysis of global stability and the convergence of the overall system with a self-tuning model. Compared with the stability results of WMMAC in the early stage, the constraint condition that the model set only has fixed models is relaxed, which can enlarge the application range of the stability results in theory. In addition, because of the introduction of a self-tuning controller, the control performance of the system is significantly improved when the real model of the plant is not included in the model set. Finally, computer simulation results verify the feasibility and effectiveness of the proposed method.