Chaos in dynamical systems is still considered to be a somewhat curious, and generally undesirable property of nonlinear systems. Despite the plethora of chaotic control methods published over the last decades, only in a few instances has the control of chaos been used to address real world problems in engineering or medicine. This is partly due to the limits of the used control methods, which either require specific analytical knowledge of the system, or the system needs to have specific characteristics to be able to be controllable. The lack of solutions for engineering and biomedical problems may also be due to specific requirements that prevent the implementation of control methods and the, as yet unproven, benefits that controlled chaos may bring to these problems. The aim of a practical application of chaos control is to fully control chaos in theoretical problems first, and then show applicable solutions to physical problems of stability and control. This controlled chaotic state should then have clear and distinct dynamic advantages over uncontrolled chaos and steady state systems. The application of the Rate Control of Chaos (RCC) method, which is derived from metabolic control processes, has already been shown to be effective in controlling several engineering problems. RCC allows non-linear systems to be stabilised into controlled oscillations, even across bifurcations, and it also allows the system to operate in regions of the parameter space that are inaccessible without this method of control. For fun, I will show that RCC controls the N-Body problem; for profit, that it can control a bioreactor model to greatly improve yield. The RCC method promises to, finally, permit the control of complex dynamic systems.
olde Scheper, T.V.
Faculty of Technology, Design and Environment\School of Engineering, Computing and Mathematics