Decoupled fixed point transformation based adaptive control of the generalized 2 DOF Φ6-type Van der Pol oscillator

In this paper a possible application of a novel adaptive control approach is reported that fits to the “traditional line of thinking” according to which in the most practical cases neither very precise, nor even complete system model is needed for obtaining precise control for dynamical systems. The validity of this statement is briefly pointed out in the most popular approaches as the main idea of the Robust Sliding Mode / Variable Structure Controllers, in Lyapunov's
^2nd
Method, and in a recently published problem tackling based on the simple geometric interpretation of the Singular Value Decomposition. In the present approach differential equations are deduced from iterative Cauchy sequences to realize adaptive control of a coupled nonlinear system in “decoupled manner”, using single dimensional projections of the “acceleration space”. The paradigm on which the method is demonstrated is a 2 dimensional generalization of the originally single dimensional Φ
⁶
-type Van der Pol oscillator that is a popular paradigm of chaotic systems. Further possible generalizations of the novel method is outlined, too.