Adaptive polynomial identification and robust optimal tracking control for nonlinear systems

This paper proposes an adaptive polynomial identifier and a robust optimal tracking control scheme for polynomial systems. In order to approximate the dynamics of an uncertain and disturbed nonlinear system, it is proposed a polynomial identifier whose parameters are on-line adapted by an adaptation algorithm based on the measurement of only one of the variables that constitute the system. Then, based on the polynomial identifier, an infinite-time state-feedback optimal tracking controller is synthesized, which includes an integral term to provide robustness to the control strategy. The effectiveness of the proposed identifier-controller strategy is illustrated via simulation for the identification and control of the blood glucose-insulin system by using the Bergman model (BeM) to describe the dynamics of type 1 diabetic patients.