An algebraic approach for the reconstruction of Chua's system

An algebraic approach is proposed for the fast, accurate, identification of the unknown parameters in Chua's chaotic oscillator. The proposed algorithm uses the availability of two measurable output voltage signals and produces an exact formula for the unknown parameters, which may be realized in terms of iterated convolutions. We show that Chua's system parameters are linearly identifiable, with respect to the two proposed measurable outputs, thus allowing us to obtain a linear system for the unknown parameters from where these unknowns are readily obtained. Suitable algebraic operations on the output differential equations make the proposed algorithm independent of the unavailable initial conditions of the underlying nonlinear dynamical system and robust with respect to high frequency output measurement noises. Suitable algorithm reinitialization, or resetting of the integrations, allow for the efficient computation of piecewise constant varying parameters. Convincing computer simulations are presented and discussed.