A note on state and parameter estimation in a van der Pol oscillator

An exact observer approach for simultaneous state and parameter estimation is proposed for the well-known van der Pol oscillator. The approach is based on an appropriate state space representation–using the so-called Liénard transformation–allowing for an exact Kalman-like observer design. The stability is then formally checked relying on the natural oscillatory behaviour of the system, and the corresponding results are illustrated in simulation.