Controlling the global behavior of coupled chaotic systems by means of energy regulation

This paper addresses the problem of partially controlling a set of two unidirectionally coupled, nonlinear (possibly chaotic) subsystems in order that the whole system performs some stable behaviors of interest. In this purpose, the proposed approach mainly consists in regulating the whole system energy (implicitly related to system trajectories), by means of an Energy based Sliding Mode Control scheme (ESMC for short), so that this energy converges towards a neighborhood of a selected magnitude. A major point is that the designed control inputs are directly applied to the master system, contrarily to usual approaches which generally consider the control of slave subsystems (or both master and slave subsystems). In this paper, we introduce some theoretical results related to the proposed approach. Then, an example involving two unidirectionally coupled Chuaʹs circuits is presented.