Practical time-varying formation tracking for high-order nonlinear multiagent systems with multiple leaders based on the distributed disturbance observer

Practical time-varying formation tracking analysis and design problems for high-order nonlinear multiagent systems with directed interaction topologies are investigated by using the distributed disturbance observer, where the time-varying formation tracking error can be controlled within an arbitrarily small bound. Different from the previous work, there exists a predefined time-varying formation formed by the states of the followers and the formation tracks the convex combination of the states of the leaders with unknown control inputs. Besides, the leaders can be multiple, and the dynamics of each follower has heterogeneous nonlinearity and disturbance. First, a distributed disturbance observer-based practical time-varying formation tracking protocol is constructed using neighboring relative information, where only a part of the followers, which are named as well-informed ones, are required to obtain the information of the multiple leaders. The proposed protocol can process the heterogeneous nonlinearity, the disturbance of each follower, and the unknown control inputs of the leaders simultaneously. Then, an algorithm with 2 steps is presented to design the practical time-varying formation tracking protocol by solving an algebraic Riccati equation and an algebraic equation, where the time-varying formation tracking feasibility condition is introduced. Moreover, the stability of the closed-loop multiagent system under the proposed protocol is proved by using the properties of the Laplacian matrix and the Lyapunov stability theory. Finally, a numerical simulation example is provided to illustrate the effectiveness of the obtained theoretical results.