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The finite‐time nonlinear placement problem of networked Euler‐Lagrange systems (NELSs) is discussed in this paper. The problem is reformulated into a finite‐time aggregate game under an undirected graph. Then, several novel practical gradient‐based finite‐time hierarchical (GFTH) algorithms composed of a game layer, a Nash equilibrium (NE) seeking layer, and a control layer are proposed. Specifically, the game layer employs an aggregate function to reach a consensus on the potential aggregate value which is adopted by a gradient‐based finite‐time method to tackle the finite‐time NE seeking problem in the NE seeking layer, and then, the tracking problem is realized in the control layer. The convergence results are established by a nonsmooth Lyapunov function. In addition, the versatility of the GFTH algorithms is shown by extending to address the task‐space control problem of NELSs. The effectiveness of the proposed algorithms is illustrated via simulations.

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This paper is concerned with the fixed-time formation-containment control (FTFCC) problem for networked Euler-Lagrange systems (NELSs) with unknown dynamics and disturbances. A systematically adaptive control scheme is established to address the above problems. Specifically, to reduce controller update frequency and conserve resources, a novel FTFCC algorithm via event-triggered mechanism is firstly designed to drive some agents named as leaders to form a specific configuration, and simultaneously the others named as followers are forced into the structured convex hull formed by leaders. Then, to eliminate the negative effects of input saturation, another algorithm by extending the proposed FTFCC algorithm is designed to deal with the problem of NELSs with saturation constraints. The key feature of the proposed algorithms is that adaptive neural networks with ε-modification updating laws are employed to approximate the unknown dynamics. It is proved by Lyapunov stability analysis that error signals would converge to a compact set near the origin within a fixed time. Furthermore, the lower bound of the trigger time interval can be calculated to rule out Zeno behaviors. Finally, the effectiveness of the proposed algorithms is verified by several numerical simulations.