Nonlinear placement for networked Euler‐Lagrange systems: A finite‐time hierarchical approach

Abstract

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.

Hierarchical Nash equilibrium seeking strategies of quadratic time‐varying games with Euler–Lagrange players

“…Similar to References 4,5,16,18, and 23, some general assumptions and lemmas are presented as follows.…”

“…In summary, the main contributions can be summarized as follows. Compared with most existing works on distributed games, 7,10,23 this article studies the seeking problems for time‐varying Nash equilibrium that is more general in practice. Note that, the previous mentioned methods might be challengeable to realize a quick response performance for the time‐varying Nash equilibrium seeking.…”