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In any drive system, there are always couplings between the motor and the load. Since the hardness of these couplings is finite, they have elastic properties, causing unwanted vibration and negatively affecting system quality. When the couplings are springs with nonlinear characteristics, control is particularly difficult because it is very difficult or impossible to define the parameters of the controlled object. To solve these difficulties, this article proposes an adaptive controller of the major functions for controlling a drive system with nonlinear elastic couplings of unidentified parameters. For the proposed control system, we measure the response speed of the object, use a Luenberger observer to estimate the state variables of the system, and use an adaptive controller to control the system. The experimental results demonstrate that the control object can be controlled without knowing the parameters: the control quality of the system is very good, close to that of a system with a hard coupling, there is no vibration or overshoot, and the transition time is small.

Based on Lyapunov theory, this research demonstrates the stability of the sliding surface in the consensus problem of multi-agent systems. Each agent in this system is represented by the dynamically uncertain robot, unstructured disturbances, and nonlinear friction, especially when the dynamic function of agent is unknown. All system states use neural network online weight tuning algorithms to compensate for the disturbance and uncertainty. Each agent in the system has a different position, and their trajectory approach to the same target is from each distinct orientation.In this research, we analyze the design of the sliding surface for this model and demonstrate which type of sliding surface is the best for the consensus problem. Lastly, simulation results are presented to certify the correctness and the effectiveness of the proposed control method.

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