Stabilization of global invariant sets for chaotic systems: An energy based control approach

This paper presents a new control approach for steering trajectories of three-dimensional nonlinear chaotic systems towards stable stationary states or time-periodic orbits. The proposed method mainly consists in a sliding mode-based control design that is extended by an explicit consideration of system energy as basis for both controller design and system stabilization. The control objective is then to regulate the energy with respect to a shaped nominal representation implicitly related to system trajectories. In this paper, we establish some theoretical results to introduce the control design approach referred to as Energy based Sliding Mode Control (ESMC for short). Then, some capabilities of the proposed approach are illustrated through examples related to the chaotic circuit of Chua.