Formation control with disturbance rejection for a class of Lipschitz nonlinear systems

Abstract

In this paper, we consider the leader-follower formation control problem for general multi-agent systems with Lipschitz nonlinearity and unknown disturbances. To deal with the disturbances, a disturbance observer-based control strategy is developed for each follower. Then, a time-varying formation protocol is proposed based on the relative state of the neighbouring agents and sufficient conditions for global stability of the formation control are identified using Lyapunov method in the time domain. The proposed strategy and analysis guarantee that all signals in the closed-loop dynamics are uniformly ultimately bounded and the formation tracking error converges to an arbitrarily small residual set. Finally, the validity of the proposed controller is demonstrated through a numerical example.

Formation control with obstacle avoidance of second-order multi-agent systems under directed communication topology

“…which implies L T ∆ + ∆L is a zero row-sum matrix. According to Lemma 3, Γ = L T ∆ + ∆L + 2∆B is a positive definite matrix, and thus αΓ − ∆ > 0 is guaranteed when the design constant α satisfies (19). Hence V (t) is a positive definite function.…”

“…Theorem 1. The multi-agent system (1) is with bounded initial states under the strongly connected graph G. If the following condition (19) for parameters α and β k , k = 1, . .…”

“…First, the function (20) can be positive definite if the condition (19) holds. It is proven as follows.…”

“…By choosing the control parameter α to satisfy the condition (19), the matrix αΓ − In αΓ − 2∆ − In , and let γ 2 be the maximum eigenvalue of the matrix ∆ T ∆ 0 n×n 0 n×n ∆ T ∆ , i.e., γ 2 = 2max{σ 2 1 , . .…”

“…With the development of multi-agent control, several excellent consensus methods have been extended to multi-agent formation. For example, multi-agent systems have been proposed for single integrated dynamics [16][17][18][19] and double integrated dynamics [20,21]. First-order multi-agent formation must only maintain a constant formation velocity, but the second-order case is more complex and requires difficult treatment of the time varying velocity.…”