Output feedback form of Chua’s circuit and modular adaptive control of chaos using single measurement

The paper treats the question of the representation of the Chua’s circuit in an output feedback form and then derives an adaptive control system for the control of chaos by a single output (node voltage) feedback. The design is performed under the assumption that all the circuit parameters are unknown, but only the lower bound on the coefficient of virtual control input and its sign are given. Based on the output feedback form of the Chua’s circuit, certain filters are designed for the estimation of the state variables. The derived controller has a modular structure consisting of an input-to-state stabilizing (ISS) control module and a passive parameter identifier. In the closed-loop system, output trajectory control is accomplished and the state vector converges to the equilibrium point. Simulation results are presented which show that the designed control system regulates the node voltage to the reference point and suppresses the chaotic motion using a single node voltage feedback.