Observer-based adaptive time-varying formation tracking of one-sided Lipschitz nonlinear multi-agent systems

Practical time-varying formation tracking problems for second-order nonlinear multiagent systems with multiple leaders are investigated using adaptive neural networks (NNs), where the time-varying formation tracking error caused by time-varying external disturbances can be arbitrarily small. 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 dynamics of each agent has both matched/mismatched heterogeneous nonlinearities and disturbances simultaneously. First, a practical time-varying formation tracking protocol using adaptive NNs is proposed, which is constructed using only local neighboring information. The proposed control protocol can process not only the matched/mismatched heterogeneous nonlinearities and disturbances, but also the unknown control inputs of the leaders. Second, an algorithm with three steps is introduced to design the practical formation tracking protocol, where the parameters of the protocol are determined, and the practical time-varying formation tracking feasibility condition is given. Third, the stability of the closed-loop multiagent system is proven by using the Lyapunov theory. Finally, a simulation example is showed to illustrate the effectiveness of the obtained theoretical results.

Time-varying formation tracking problem for single-integrator multi-agent system with one leader and several followers on directed graphs are investigated. The followers need to achieve predefined time-varying formation while tracking the leader with unknown control input. Firstly, a time-varying formation tracking control protocol is designed by using neighbor information. Then based on the Lyapunov theory, a proof that the multi-agent systems can achieve the desired time-varying formation tracking is given. Furthermore, a simulation example of formation tracking motion of multi-agent systems composed of three followers and one leader under designed protocol is given. Finally, the protocol is applied to a unmanned ground vehicle(UGV) systems composed of one leader and three followers to demonstrate the effectiveness of the theoretical results.

In this paper, time-varying formation tracking problem for second-order nonlinear multi-agent systems with time-varying communication delays has been investigated, where the followers maintain a predefined time-varying formation while tracking the moving leader. Based on a distributed observer, a formation tracking protocol with time-varying delay is developed using the relative neighboring information. By constructing the Lyapunov-Krasovskii (L-K) function, sufficient conditions have been obtained to guarantee the stability of time-varying formation tracking. In addition, the unknown gain matrix in the proposed protocol is computed out through the technique of variable substitution. Numerical simulation results are presented to validate the effectiveness of our theoretical analysis.

A new event-triggered distributed state estimation approach for one-sided Lipschitz nonlinear discrete-time systems and its application to wireless sensor networks

Time-varying formation tracking analysis and design problems for second-order multi-agent systems with one leader are studied respectively, where the states of followers form a predefined time-varying formation while tracking the state of the leader. A formation tracking protocol is constructed using only neighboring relative information. Necessary and sufficient conditions for second-order multi-agent systems with one leader to achieve time-varying formation tracking are proposed by utilizing the properties of the Laplacian matrix, where the formation tracking feasibility constraint is also given. An approach to design the formation tracking protocol is proposed by solving an algebraic Riccati equation. The presented results can be applied to deal with the target enclosing problems and consensus tracking problems for second-order multi-agent systems with one target/leader. An application in the target enclosing of multiple vehicles is provided to demonstrate the effectiveness of the theoretical results.

In this paper, the time-varying formation (TVF) tracking problem is studied for multi-agent systems (MAS) with the leader’s control input is nonzero. First assuming that the agents’ states are unavailable, the state observer is therefore designed to deal with this situation. Then, a novel kind of event-triggered (ET) adaptive output feedback TVF tracking controller for linear MASs is put forward. According to Lyapunov stability theory, the result implies that under the appropriate assumptions the proposed controller is implementable without using any global information. Furthermore, for the designed ET condition, Zeno behavior doesn’t manifest in any agent. Furthermore, numerical simulation is given to validate the performance of the design techniques.

This article investigates the practical time-varying output formation tracking (TVOFT) problem for heterogeneous nonlinear multiagent systems (MASs) having multiple leaders, where agents herein could have heterogeneous dynamics and interact with each other under event-triggered communications. It is required that the outputs of followers not only track the predefined convex combination of multiple leaders but also achieve the desired time-varying formation simultaneously. The existing works on formation tracking problems for MASs with multiple leaders depend on the assumption that each follower is a well-informed or uninformed follower, where the well-informed follower is required to have all the leaders as its neighbor. To remove the limitation, a fully distributed observer-based formation tracking control protocol is developed and employed. First, an adaptive state observer with an edge-based event-triggered mechanism for estimating the states of multiple leaders is proposed based on the neighboring interactions, which eliminates the unexpected Zeno behavior. Second, a novel observer is constructed for each follower by exploiting the output information of the follower, in which the adaptive neural network (NN)-based approximation is exploited to compensate for the unknown nonlinearity. A practical TVOFT control protocol is then generated by the proposed observers, where the parameters are determined by an algorithm including five steps. With the help of Lyapunov stability theory and output regulation method, a practical TVOFT criterion for the considered closed-loop system is derived. Finally, the effectiveness of the proposed control scheme is illustrated by a numerical example.

Time-varying formation tracking problems for unmanned aerial vehicle (UAV) swarm systems with switching interaction topologies are studied, where the states of the follower UAVs form a predefined time-varying formation while tracking the state of the leader UAV. A formation tracking protocol is constructed using only relative information of neighboring UAVs. An approach to design the formation tracking protocol is proposed by solving an algebraic Riccati equation, and the stability of the proposed approach is proven using the common Lyapunov stability theory. The obtained results are applied to solve the target enclosing problem of a quadrotor swarm system consisting of one leader (target) quadrotor and three follower quadrotors. Both a numerical simulation and an outdoor experiment are presented to demonstrate the effectiveness of the theoretical results.

We investigate the distributed time-varying formation tracking of networked quadrotors with input saturation and moving obstacles. The quadrotors’ position and attitude models are subjected to unknown external disturbances. This study has two main contributions. First, we develop filter-based distributed desired profiles and extended state observers (ESOs) for state-transformed nonlinear quadrotors to achieve time-varying formation tracking without requiring the velocity and acceleration information of the leader, followers, and moving obstacles. This achievement holds even in the presence of input saturation. Second, the proposed approach guarantees collision avoidance with moving obstacles, including adjacent quadrotors and unknown objects, by using only the relative distance from the obstacle, irrespective of external disturbances. This is accomplished by designing error functions for avoiding moving obstacles and including auxiliary signals in the formation tracker design. Based on the distributed profiles and the signals estimated using the ESOs, we design a collision-free time-varying formation tracker. The Lyapunov stability theory is utilized to prove that all signals of the proposed closed-loop formation tracking system are bounded, and the tracking errors converge to an adjustable bound that includes the origin. Finally, simulation results are provided to demonstrate the effectiveness of the proposed method.

Generalized filtering of one-sided Lipschitz nonlinear systems under measurement delays

This paper considers the consensus problem of two class of multi-agent systems with communication disturbance by using iterative learning control(ILC) method and both of them has a fixed information topology with a spanning tree. Firstly, a distributed iterative learning-based control protocol is designed for a time-varying linear multi-agent system, a sufficient condition is obtained such that the consensus problem is solved. By the same way, a sufficient condition is also given for a class of nonlinear time-varying multi-agent systems to solve consensus problem. The main contribution of the proposed results is that they can restrain any type of repetitive disturbance. The validity of them is verified by the simulation results.

Time-varying formation tracking (TVFT) control problem for multiple Euler–Lagrange (EL) systems with an uncertain leader is investigated in this article. The objective of this problem is for the followers' states to track the uncertain leader's output and achieve the desired formation. One of the major challenges in solving such a problem lies in estimating the information of the leader. In this article, an observer-based TVFT control framework is presented in this article, which does not require all or part of the follower agents to know the system dynamic knowledge of the leader agent directly in advance. First, two fully distributed adaptive observers are presented for estimating the uncertain leader's state, output, and the unknown system matrices under an IE condition, which relaxes the existing restrictive persistently exciting or cooperative finite-time excitation condition. Then, on the basis of the constructed adaptive observers, state and output variables of the leader, a fully distributed TVFT for EL systems with an uncertain leader is developed, which means the proposed formation tracking controller operates independently of the system dynamic knowledge of the leader agent; with the help of the Lyapunov stability theory, the TVFT criterion for the considered system is derived. Finally, in order to demonstrate the theoretical results derived in this article, a practical air–ground formation tracking platform, which consists of an unmanned aerial vehicle and four unmanned ground vehicles, is introduced, and physical experimental results are obtained.

In this paper, the time-varying formation tracking problem of the general linear multi-agent system is discussed. A distributed formation tracking protocol based on Riccati inequalities with adaptive coupling weights among the follower agents and the leader agent is designed for a leader-following multi-agent system under fixed and switching topologies. The formation configuration involved in this paper is expressed as a bounded piecewise continuously differentiable vector function. The follower agents will achieve the desired formation tracking trajectory of the leader. In traditional static protocols, the coupling weights depend on the communication topology and is a constant. However, in this paper, the coupling weights are updated by the state errors among the neighboring agents. Moreover, the stability analysis of the MAS under switching topology is presented, and proves that the followers also could achieve pre-specified time-varying formation, if the communication graph is jointly connected. Two numerical simulations indicate the capabilities of the algorithms.

Distributed impulsive consensus of nonlinear multi-agent systems with input saturation

In this article, adaptive group time-varying formation tracking (TVFT) control problems for unmanned swarm systems are investigated based on networked distributed game. To describe the competition which commonly exists between different subgroups, a novel adaptive group TVFT control framework is designed. Specifically, the group-leaders are required to converge to the Nash equilibrium (NE) of intergroup game, meanwhile the followers within each group will simultaneously realize TVFT relative to their group-leader. In addition, benefit from the adaptive mechanism, the dependence of controller parameters on system scale, interaction topology, and cost function is eliminated. By constructing Lyapunov function with both NE seeking error and TVFT error, the stability of the coupled closed-loop swarm system is proved. An experiment platform with unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) is constructed, then both simulation and experiment results are provided to demonstrate the effectiveness of the proposed controller.