Signal flow graph and control of realizable autonomous nonlinear Chen model with quaternion variables

Abstract

In this work, we continue our study of autonomous nonlinear dynamical systems with quaternion variables. We present a novel chaotic Chen system with quaternion variables. This system in real form is high (nine) dimensional. We study the dynamics and basic properties of this model with quaternion variables. We also evaluate the stability of the trivial points and restrict the conditions under which the nonlinear novel quaternion Chen system has negative, zero, or positive Lyapunov exponents. A signal flow graph and an electronic circuit implementation are designed, analyzed, and constructed to realize the novel Chen system. The control problem of chaotic nonlinear systems with quaternion variables is investigated. We propose and design an approach to build a controller for these systems. The viability and usefulness of the suggested approach are illustrated by an application to the chaotic Chen model with quaternion variables. Using the proposed method, the attractors of the quaternion Chen model are transformed to trivial fixed point, quasi-periodic, or periodic (limit cycle) states. The mathematical results for the controller according to this method are confirmed numerically.

Keywords

• Chaotic
• Control
• Signal flow graph
• Electronic circuits
• Quaternions