A family of driving forces to suppress chaos in jerk equations: Laplace domain design.

A family of driving forces is discussed in the context of chaos suppression in the Laplace domain. This idea can be attained by increasing the order of the polynomial in the expressions of the driving force to account for the robustness and/or the performance of the closed loop. The motivation arises from the fact that chaotic systems can be controlled by increasing the order of the Laplace controllers even to track arbitrary orbits. However, a larger order in the driving forces can induce an undesirable frequency response, and the control efforts can result in either peaking or large energy accumulation. We overcame these problems by showing that considering the frequency response (interpreted by norms), the closed-loop execution can be improved by designing the feedback suppressor in the Laplace domain. In this manner, the stabilization of the chaotic behavior in jerk-like systems is achieved experimentally. Jerk systems are particularly sensitive to control performance (and robustness issues) because the acceleration time-derivative is involved in their models. Thus, jerky systems are especially helped by a robust control design.