Tracking algorithms for multiagent systems

Data-Driven Adaptive Iterative Learning Bipartite Consensus for Heterogeneous Nonlinear Cooperation-Antagonism Networks

Heterogeneous dynamics, strongly nonlinear and nonaffine structures, and cooperation-antagonism networks are considered together in this work, which have been considered as challenging problems in the output consensus of multiagent systems. A heterogeneous linear data model (LDM) is presented to accommodate the nonlinear nonaffine structure of the heterogeneous agent. It also builds an I/O dynamic relationship of the agents along the iteration-dimensional direction to make it possible to learn control experience from previous iterations to improve the transient consensus performance. Then, an adaptive update algorithm is developed for the estimation of the uncertain parameters of the LDM to compensate for the unknown heterogeneous dynamics and model structures. To address the problem of cooperation and antagonism, an adaptive learning consensus protocol is proposed considering two signed graphs, which are structurally balanced and unbalanced, respectively. The learning gain can be regulated using the proposed adaptive updating law to enhance the adaptability to the uncertainties. With rigorous analysis, the bipartite consensus is proven in the case that the graph is structurally balanced, and the convergence of the agent output to zero is also proven in the case that the graph is unbalanced in its structure. The presented bipartite consensus method is data-based without the use of any explicit model information. The theoretical results are demonstrated through simulations.

Transient Bipartite Synchronization for Cooperative-Antagonistic Multiagent Systems With Switching Topologies

This article aims at addressing the transient bipartite synchronization problem for cooperative-antagonistic multiagent systems with switching topologies. A distributed iterative learning control protocol is presented for agents by resorting to the local information from their neighbor agents. Through learning from other agents, the control input of each agent is updated iteratively such that the transient bipartite synchronization can be achieved over the targeted finite horizon under the simultaneously structurally balanced signed digraph. To be specific, all agents finally have the same output moduli at each time instant over the desired finite-time interval, which overcomes the influences caused by the antagonisms among agents and topology nonrepetitiveness along the iteration axis. As a counterpart, it is revealed that the stability can be achieved over the targeted finite horizon in the presence of a constantly structurally unbalanced signed digraph. Simulation examples are carried out to demonstrate the effectiveness of the distributed learning results developed among multiple agents.

A Distributed Lyapunov-Based Redesign Approach for Heterogeneous Uncertain Agents With Cooperation-Competition Interactions

A swarming behavior problem is investigated in this article for heterogeneous uncertain agents with cooperation-competition interactions. In such a problem, the agents are described by second-order continuous systems with different intrinsic nonlinear terms, which satisfies the "linearity-in-parameters" condition, and the agents' models are coupled together through a distributed protocol containing the information of competitive neighbors. Then, for four different types of cooperation-competition networks, a distributed Lyapunov-based redesign approach is proposed for the heterogeneous uncertain agents, where the distributed controller and the estimation laws of unknown parameters are obtained. Under their joint actions, the heterogeneous uncertain multiagent system can achieve distributed stabilization for structurally unbalanced networks and output bipartite consensus for structurally balanced networks. In particular, the concept of coherent networks is proposed for structurally unbalanced directed networks, which is beneficial to the design of distributed controllers. Finally, four illustrative examples are given to show the effectiveness of the designed distributed controller.

Consensus Control for Heterogeneous Multivehicle Systems: An Iterative Learning Approach

This article investigates the consensus tracking problem of the heterogeneous multivehicle systems (MVSs) under a repeatable control environment. First, a unified iterative learning control (ILC) algorithm is presented for all autonomous vehicles, each of which is governed by both discrete- and continuous-time nonlinear dynamics. Then, several consensus criteria for MVSs with switching topology and external disturbances are established based on our proposed distributed ILC protocols. For discrete-time systems, all vehicles can perfectly track to the common reference trajectory over a specified finite time interval, and the corresponding digraphs may not have spanning trees. Existing approaches dealing with the continuous-time systems generally require that all vehicles have strictly identical initial conditions, being too ideal in practice. We relax this unpractical assumption and propose an extra distributed initial state learning protocol such that vehicles can take different initial states, leading to the fact that the finite time tracking is achieved ultimately regardless of the initial errors. Finally, a numerical example demonstrates the effectiveness of our theoretical results.

Convergence Conditions for Solving Robust Iterative Learning Control Problems Under Nonrepetitive Model Uncertainties

Learning from saved measurement and control data to refine the performance of output tracking is the core feature of iterative learning control (ILC). Even though this implementation process of ILC does not need any model knowledge, ILC typically requires the strict repetitiveness of the control systems, especially on the plant models of them. The questions of interest in this paper are: 1) whether and how can robust ILC problems be solved with respect to the nonrepetitive (or iteration-dependent) model uncertainties and 2) can convergence conditions be developed with the effective contraction mapping (CM)-based approach to ILC? The answers to these questions are affirmative, and the CM-based approach is applicable to robust ILC that accommodates certain nonrepetitive uncertainties, especially in the plant models. In particular, an H_∞ -norm condition is proposed to ensure the robust ILC convergence, which can be solved to determine learning gain matrices. Simulation tests are performed to illustrate the validity of our presented H_∞ -based analysis results.

Avoiding Congestion in Cluster Consensus of the Second-Order Nonlinear Multiagent Systems

In order to avoid congestion in the second-order nonlinear leader-following multiagent systems over capacity-limited paths, an approach called cluster lag consensus is proposed, which means that the agents in different clusters will pass through the same positions with the same velocities but lag behind the leader at different times. Lyapunov functionals and matrix theory are applied to analyze such cluster lag consensus. It is shown that when the graphic roots of clusters are influenced by the leader and the intracoupling of cluster agents is larger than a threshold, the cluster lag consensus can be achieved. Furthermore, the cluster lag consensus with a time-varying communication topology is investigated. Finally, an illustrative example is presented to demonstrate the effectiveness of the theoretical results. In particular, when the physical sizes of the agents are taken into consideration, it is shown that with a rearrangement and a position transformation, the multiagent system will reach cluster lag consensus in the new coordinate system. This means that all agents in the same cluster will reach consensus on the velocity, but their positions may be different and yet their relative positions converge to a constant asymptotically.

Data-Driven Learning Control for Stochastic Nonlinear Systems: Multiple Communication Constraints and Limited Storage

This paper proposes a data-driven learning control method for stochastic nonlinear systems under random communication conditions, including data dropouts, communication delays, and packet transmission disordering. A renewal mechanism is added to the buffer to regulate the arrived packets, and a recognition mechanism is introduced to the controller for the selection of suitable update packets. Both intermittent and successive update schemes are proposed based on the conventional P-type iterative learning control algorithm, and are shown to converge to the desired input with probability one. The convergence and effectiveness of the proposed algorithms are verified by means of illustrative simulations.

Quantized Iterative Learning Consensus Tracking of Digital Networks With Limited Information Communication

This brief investigates the quantized iterative learning problem for digital networks with time-varying topologies. The information is first encoded as symbolic data and then transmitted. After the data are received, a decoder is used by the receiver to get an estimate of the sender's state. Iterative learning quantized communication is considered in the process of encoding and decoding. A sufficient condition is then presented to achieve the consensus tracking problem in a finite interval using the quantized iterative learning controllers. Finally, simulation results are given to illustrate the usefulness of the developed criterion.

Finite-Time Consensus for Multiagent Systems With Cooperative and Antagonistic Interactions

This paper deals with finite-time consensus problems for multiagent systems that are subject to hybrid cooperative and antagonistic interactions. Two consensus protocols are constructed by employing the nearest neighbor rule. It is shown that under the presented protocols, the states of all agents can be guaranteed to reach an agreement in a finite time regarding consensus values that are the same in modulus but may not be the same in sign. In particular, the second protocol can enable all agents to reach a finite-time consensus with a settling time that is not dependent upon the initial states of agents. Simulation results are given to demonstrate the effectiveness and finite-time convergence of the proposed consensus protocols.

Robust consensus tracking control for multiagent systems with initial state shifts, disturbances, and switching topologies

This paper deals with the consensus tracking control issues of multiagent systems and aims to solve them as accurately as possible over a finite time interval through an iterative learning approach. Based on the iterative rule, distributed algorithms are proposed for every agent using its nearest neighbor knowledge, for which the robustness problem is addressed against initial state shifts, disturbances, and switching topologies. These uncertainties are dynamically changing not only along the time axis but also the iteration axis. It is shown that the matrix norm conditions can be developed to achieve the convergence of the considered consensus tracking objectives, for which necessary and sufficient conditions are presented in terms of linear matrix inequalities to guarantee their feasibility in the sense of the spectral norm. Furthermore, simulation examples are given to illustrate the effectiveness and robustness of the obtained consensus tracking results.