On Optimality of Local Control of Chaos

Local control stabilizes chaotic motions by applying a state feedback only within a possible strongly bounded state space region of control (SSRC). In this paper, we consider the question of when a local control is optimal. Therefore, a cost function is employed that accounts for two components: time and control force needed until stabilization occurs. We present analytical and numerical results on the dependency of the cost on the size of the SSRC and a weighting constant between the two components of the cost function.