On distributed finite-time observer design and finite-time coordinated tracking of multiple double integrator systems via local interactions

Abstract

SUMMARYThis paper studies finite‐time coordinated tracking problem for multiple double integrator systems with a time‐varying leader's velocity and bounded external disturbances. We consider the dynamic feedback designs for two different cases. In the first case, the velocities of the followers and the leader are assumed to be unavailable, and the communication topology is assumed to be undirected and fixed. In the second case, the velocities of the followers and the leader are assumed to be available, and the communication topology is assumed to be directed and switching. Distributed finite‐time observers are designed, respectively, to obtain the velocity information in the first case and the relative state information in the second case. The states of these observers are then used to design control inputs that achieve finite time robust coordinated tracking of multiple double integrator systems in the presence of bounded disturbances for these two cases. Simulation results are provided to validate the effectiveness of these theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.

Distributed finite‐time formation control for multiple quadrotors via local communications

“…(i) Novel distributed finite‐time state observers are designed to estimate the relative state error between leader and followers. Compared with the previous work, the state observer has faster convergence rate. (ii) Finite‐time control law is designed for the position subsystem based on the values of the observers such that all quadrotors can converge to the desired 3D‐pattern and move along the desired leader's trajectory in a finite time.…”

“…Under the condition that Assumption 2 holds, it is trivial to show that W 1 ( ε hu ) ≥ 0 and W 1 ( ε hu )=0 if and only if ε hu 0 = ε hu 1 =···= ε hun =0 from the facts that and . Motivated by Meng et al, we construct the following sets: , . Following a similar analysis as in the proof of theorem 1 of Andreasson et al, it is trivial to show that, under the condition that Assumption 2 holds, S 1 ∪ S 2 ≠∅ for the case of W 1 ( ε hu )>0.…”

Terminal sliding mode control based finite-time coordinated tracking for disturbed high-order integrator systems

“…In [18], the authors proposed a finite-time consensus protocol for second-order integrator systems with unknown inherent nonlinear dynamics under undirected switching interaction graphs. In [19,20], observer-based finite-time coordinated tracking problem for double and high-order integrator systems with bounded external disturbances were studied, respectively. In [21], a multi-surface sliding mode cooperative control scheme was presented to solve the finite-time coordinated tracking problem for a class of high-order integrator systems with bounded input disturbances.…”

“…Note that most of the existing works on finite-time coordination problems have focused on simple dynamics such as first-order or second-order integrator systems [9][10][11][12][13][14][15][16][17][18][19], and the results are usually applicable under the assumption that the dynamics of the agents are exactly known. In practical situations, many systems are modeled by high-order nonlinear dynamics and system uncertainties and input disturbances often arise in many control engineering applications [22,23].…”

“…In view of the existing results on finite-time coordinated tracking problems, the advantages of our strategies mainly lie in the following aspects. First, compared with [9][10][11][12][13][14][15][16][17][18][19], which focused on first-order or second-order dynamic systems, our results are applicable for much wider classes of systems under general communication topologies. Second, unlike the protocols presented in [14,21] where exchanges of control inputs between neighboring agents are needed or the protocols in [19,20] which required communication of relative observer states, only relative measurements are needed in the proposed control strategies.…”