Nonlinear Model Reference Adaptive Control with Embedded Linear Models

Abstract

We propose a nonlinear model reference adaptive control strategy in which a linear model (or a set of linear models) is embedded within the nonlinear controller. The technique is applicable to single-input, single-output nonlinear processes with stable zero dynamics and full-state feedback. The nonlinear control law is constructed by embedding linear controller gains obtained from a linear model or multiple linear models. The higher-order controller functions are approximated with locally supported radial basis functions centered in the state space. The number of basis functions is determined a priori, and an on-line pruning algorithm is utilized to ensure functions centered near the current operating point are active. Parameter update laws that guarantee (under certain assumptions) that the plant output asymptotically tracks the output of a linear reference model and the state vector remains bounded are derived via Lyapunov stability analysis. The proposed control strategy is compared to a linear state feedback controller and a linear multimodel adaptive controller using a nonlinear chemical reactor model.