Robust second‐order finite‐time formation control of heterogeneous multi‐agent systems on directed communication graphs

Distributed finite‐time formation control of multiple Euler–Lagrange systems under directed graphs

“…In [21], a finite-time consensus controller was designed based on the homogeneous theory such that multiple underactuated spacecrafts described by Euler-Lagrange equations could track a stationary leader under undirected topology. In [22], finite-time formation of heterogeneous second-order systems was established based on the technique of adding a power integrator. In [23], the finite-time coordination behaviour for the case where multiple Euler-Lagrange systems are in cooperation-competition networks was investigated by combining the technique of adding a power integrator with the homogeneous theory.…”

“…(3) Fractional powers contained in the proposed controller are only related with the constructed auxiliary state, the number of which has no concern with the number of agents engaging into coordination behaviours and the dimension of system dynamics describing the agents. By contrast, most existing controllers contain fractional powers of system states, sliding mode variables and transformed variables as reviewed in [16][17][18][19][20][21][22][23][24][25], where the number of fractional power terms is sensitive to the number of agents and the dimension of system dynamics mentioned above. (4) Dynamic surface control is improved to facilitate finite-time controller design without using acceleration information.…”

“…By contrast, symmetric connection of undirected topology is assumed in many existing works such as [17–19, 21 23, 25], where symmetric Laplacian matrices were adopted to construct Lyapunov functions, and thus matrix operations were applied to reduce controller design complexity largely. (3)Fractional powers contained in the proposed controller are only related with the constructed auxiliary state, the number of which has no concern with the number of agents engaging into coordination behaviours and the dimension of system dynamics describing the agents. By contrast, most existing controllers contain fractional powers of system states, sliding mode variables and transformed variables as reviewed in [16–25], where the number of fractional power terms is sensitive to the number of agents and the dimension of system dynamics mentioned above. (4)Dynamic surface control is improved to facilitate finite‐time controller design without using acceleration information. By contrast, conventional dynamic surface control as presented in [30] is inapplicable to finite‐time control problems.…”

Finite‐time adaptive output synchronization of uncertain nonlinear heterogeneous multi‐agent systems

“…Finite‐time control of MASs under unknown exosystem dynamics and uncertain followers' dynamics demands new developments. The finite‐time control of second‐order heterogeneous MASs 36,37 and high‐order heterogeneous MASs 38,39 are studied. While finite‐time output formation‐tracking control of linear heterogeneous MASs is considered in Reference 25 and finite‐time 26 and fixed‐time 40 output bipartite consensus of linear heterogeneous MASs are investigated, uncertainties on exosystem dynamics and followers' dynamics are ignored.…”

Formation Tracking Control for Multi-Agent Networks with Fixed Time Convergence via Terminal Sliding Mode Control Approach

“…Coordinated control for multi-agent networks has been studied with more and more attention recently owing to its diversified application value, such as consensus [ 1 , 2 , 3 ], formation [ 4 , 5 , 6 ], containment [ 7 , 8 ], flocking [ 9 , 10 ] and tracking [ 11 , 12 ] control problems. In [ 13 ], the synchronization control problem of multi-agent networks is solved by using chaos theory and the result is applied to the coupling circuits.…”