Chaos formation and reduction in robust fixed point transformations based adaptive control

Abstract

In the design of adaptive controllers for roughly modeled nonlinear dynamic plants the most popular prevalent fundamental mathematical tool is Lypunov's “direct” method. Though normally it guarantees global stability several controller performance parameters of practical engineering significance cannot directly be addressed in this manner. In general simulation investigations or GA-based parameter optimization is needed for refining the controller. A possible alternative of the Lyapunov function technique is the application of Robust Fixed Point Transformation (RFPT) that has only local region of convergence but directly addresses practical needs as error relaxation. In this paper the details of quitting the region of convergence and its consequences are investigated. In the control of a 2 Degree Of Freedom (DOF) paradigm it will be shown that though this process has chaotic features it does not has drastic consequences in the control quality. Furthermore, it also is shown that by a simple smoothing trick this chaos can be refined and reduced to a limited amplitude of chattering that much probably is tolerable in many practical applications.