A simple control technique for partial and complete parameter identification of the chaotic Lorenz system

A simple linear state feedback control algorithm that requires tuning of a single gain is used for identifying uncertain parameters of the chaotic Lorenz system. The goal of the controller is to force the closed-loop system to reach a stable steady state with real non-zero values such that the parameters of the Lorenz system can be found algebraically and without the need to design dynamic parameters update laws. Two cases are considered to investigate both complete and partial identification of the parameters, depending on accessibility to the complete or partial state vector of the Lorenz system. In addition, extension to the hyperchaotic case is investigated to demonstrate the versatility of the proposed technique. The paper also demonstrates that synchronization-based state observers can be augmented to the state feedback controller when using a single scalar time series in the design. Hardware implementation is investigated, while highlighting the advantages and limitations of the proposed technique.