In this paper, we study the distributed Nash equilibrium (NE) seeking problem for a class of aggregative games with players described by uncertain perturbed nonlinear dynamics. To seek the NE, each player needs to construct a distributed algorithm based on information of its cost function and the exchanging information obtained from its neighbors. By combining the internal model principle and the average consensus technique, we propose a distributed gradient-based algorithm for the players. This paper not only assures the NE seeking of aggregative games but also achieves the disturbance rejection of external disturbances.

In this technical note, we consider the finite-time consensus and tracking problems for a class of nonlinear multi-agent systems with directed topology. By using the homogeneous system theory, we firstly give a finite-time consensus protocol for high-order linear multi-agent systems. Then, we present the finite-time consensus and tracking protocols for strict feedback nonlinear multi-agent systems. When state information is not available, the finite-time convergent observer is used to estimate each agent' states, and we give the finite-time consensus and tracking protocols based on the finite-time observers.

Automatic 3D navigation control of microrobot in large microenvironment is one of the primary challenges hindering its applications. In this article, we present a systematic approach to use an electromagnetic manipulation system to deal with this challenge. Two movable orthogonal microscopic cameras scan the microenvironment on the top view and side view to build a stereo occupancy map automatically. The initial position of microrobot can be located on the basis of the similarity curves generated by the scanning sequences. In accordance with the distribution characteristic of electromagnetic fields in workspace, an enhanced rapidly exploring random tree algorithm is proposed to avoid obstacles in the complex environment. To ensure continuous visual servo in wide range, a field-of-view tracking method is developed using a specific image definition evaluation algorithm. A prescribed performance controller with disturbance observer is designed, which guarantees that the microrobot can remain in the view of microscopic cameras, and the transient and steady-state performance of the system can satisfy the expected requirements. A set of experiments are performed to verify the effectiveness of the proposed automatic 3D navigation strategy. Experimental results show that the microrobot can navigate automatically in a $\boldsymbol{12}\,\times 10\,\times \text{10-mm}$ microenvironment containing obstacles, and achieve reliable field-of-view tracking and path following at high speed.