Adaptive control and synchronization of a modified Chua's circuit system.
The problem of chaos control is considered for the modified Chua circuit \[ x'=p(y-\frac{1}{7}(2x^3 -x )), \qquad y' = x-y+z, \qquad z=-qy. \] Conditions are given for the asymptotic stabilization of a fixed-point in the presence of the feedback control term \(-k(x-\bar x)\), which is introduced in the equation for the \(x\) variable. \(\bar x\) is the \(x\)-component of the fixed-point under consideration. This point is shown to be unstable in the absence of a controller. Then, the author derives conditions for the stabilization of the fixed-point in the presence of adaptive controller \(-g(x-\bar x)\), where \(g\) is updated according to the following algorithm \(g'=\gamma (x-\bar x)^2\). Finally, adaptive synchronization of two unidirectionally coupled identical Chua systems is considered.
scientific article; zbMATH DE number 1861330