This work studies logic-based distributed switching control for nonlinear agents in power-chained form, where logic-based (switching) control arises from the online estimation of the control directions assumed to be unknown for all agents. Compared to the state-of-the-art logic-based mechanisms, the challenge of power-chained dynamics is that in general asymptotic tracking cannot be obtained, even for a single agent. To address this challenge, a new logic-based mechanism is proposed, which is orchestrated by a dynamic boundary function. The boundary function is decreasing in-between switching instants and monotonically increasing at the switching instants, depending on the jumps of an appropriately designed Lyapunov-like function. To remove chattering (i.e. two or more switching instants occurring consecutively with zero dwell time), a dynamic threshold is proposed, based on selecting the maximum values of the Lyapunov-like function before and after switching.

For the pure feedback systems with uncertain actuator nonlinearity and non-differentiable non-affine function, a novel adaptive neural control scheme is proposed. Firstly, the assumption that the non-affine function must be differentiable everywhere with respect to control input has been canceled; in addition, the proposed approach can not only be applicable to actuator input dead zone nonlinearity, but also to backlash nonlinearity without changing the controller. Secondly, the neural network (NN) is used to approximate unknown nonlinear functions of system generated in the process of control design and a nonlinear robust term is introduced to eliminate the actuator nonlinearity modeling error, the NN approximation error and the external disturbances. Semi-globally uniformly ultimately boundedness of all signals in the closed loop system is analytically proved by utilizing Lyapunov theory. Finally, the effectiveness of the designed method is demonstrated via two examples.