Consensus Control for Multiple Euler-Lagrange Systems Based on High-Order Disturbance Observer: An Event-Triggered Approach

Distributed adaptive consensus protocol for heterogeneous nonlinear uncertain multi‐agent system with disturbance

“…In Rkma et al, 44 the unknown disturbance is assumed to yield the Lipschitz condition, which is $$$ \mid {f}_i\left(\boldsymbol{x}\right)-{f}_j\left(\boldsymbol{x}\right)\mid \le {\overline{l}}_{ij}\left\Vert {\boldsymbol{x}}_i-{\boldsymbol{x}}_j\right\Vert $$$, where $$$ {\boldsymbol{x}}_i $$$ and $$$ {\boldsymbol{x}}_j $$$ are the state vector of agents $$$ i $$$ and $$$ j $$$ respectively. Similar to Wu et al, 32 gain $$$ {\delta}_i $$$ in the proposed control law is chosen as $$$ {\delta}_i>\max \left\{\frac{\epsilon_1}{\rho_{1i}},\frac{\epsilon_2}{\rho_{2i}}\right\} $$$, where $$$ {\epsilon}_1 $$$ and $$$ {\epsilon}_2 $$$ are nonnegative Lipschitz constants for nonlinearities; In Guo et al, 33 the gain …”

“…And Wu et al 32 selected an appropriate gain based on the Lipschitz constant of nonlinear perturbations. Guo et al 33 obtained gain through communication topology structure. Unfortunately, it commonly cannot be estimated in advance.…”

“…, where 𝜖 1 and 𝜖 2 are nonnegative Lipschitz constants for nonlinearities; In Guo et al, 33 the gain k > 2𝜎||WH|| 2…”

Finite-Time Containment Control for Multiple Euler-Lagrange Systems Based on Disturbance Observer: A Discrete-Time Case

“…In what follows, the dynamic equation with corresponding model parameters and external disturbance for the followers are the same as those in [8]. In addition, we define the dynamic of three leaders as…”

“…Finally, the effectiveness of the theoretical results is illustrated by the simulation examples.Among the various topics related to coordination control [1-3], containment control for multi-agent systems has received much attention from systems and control communities. Compared with tracking control, which only has one leader (see [4][5][6][7][8][9]), a distinct feature of containment control…”