Asymptotic stabilization with group-wise sparse input based on control Lyapunov function approach

This study proposes a novel stabilizing controller for nonlinear systems using group-wise sparse inputs. The input variables are divided into several groups. In the situations when the input constraints can be ignored, one input becomes active for each group at each moment. Our method improves energy efficiency, as sparse input vectors often reduce the standby power of inactive actuators. Large-scale systems, such as those consisting of multiple subsystems, often require the manipulation of multiple inputs simultaneously to be controlled. Our method can be applied to such systems due to the group-wise sparsity of the inputs. The proposed controller is based on the control Lyapunov function approach and includes Sontag's universal formula as a special case. The controllers designed in our method have best-effort property, which means even when a restriction for the decreasing rate of the Lyapunov function cannot be fulfilled, the controller minimizes the time derivative of the Lyapunov function within the input constraint. The effectiveness of the proposed method can be confirmed through simulations