Distributed Adaptive Affine Formation Control for Heterogeneous Linear Networked Systems

Abstract

This paper addresses the distributed adaptive affine formation protocol design problem for the heterogeneous leader-follower-type linear networked systems, in which the interaction graph is directed. Compared with the existing methods, the affine formation control has the superiority to tackle the motion constraints of the target formation based on the affine transformation in the arbitrary dimensional space. This transformation has the property of acting as a linear transformation, and the complexity of formation controllers can be reduced. Only the partial information of the graph can be acquired by the agents, and the adaptive algorithms are adopted to find the corresponding bounds of the control gains. By introducing the additive functions for both proportional and integral terms, a distributed adaptive proportional-integraltype control algorithm of achieving the affine formation is presented. This distributed control scheme can eliminate the steady-state errors based only on the relative states of neighboring agents. The corresponding numerical simulations are carried out to verify the theoretical results; numerous types of formation patterns can be obtained.INDEX TERMS Affine formation control, heterogeneous multi-agent systems, directed graph, adaptive algorithms.

Optimal leader‐follower affine formation control of linear multi‐agent systems

“…Different from Reference 34, the dynamics of the leaders are considered as the form of ( 13). Moreover, to optimally stabilize the dynamics of tracking error system (18), we proposed a PI control law (19), which yields the different performance index ( 24) as compared to Reference 34. In addition, the limitation of inverse optimal control is that the performance indicators cannot be flexibly given, but determined by the proposed control law.…”

“…To guarantee followers can track their target positions, the error dynamical system (18) should asymptotically converge to the origin. Now, we present the main result which gives sufficient conditions for the global optimality of the linear control law (19).…”

“…Moreover, the work in Reference 18 studies the affine formation control problems with time‐varying delays. In addition, proportional‐integral control law is proposed in Reference 19 to achieve an affine formation. The affine formation control law with a sliding‐mode estimator is also developed in Reference 20.…”

Adaptive NN Control for Nonlinear Multi-Agent Systems With Unknown Control Direction and Full State Constraints

“…In the leaderless systems, an adaptive distributed controller is designed to deal with the uncertainty in the systems, and Lyapunov function is used to prove the stability of the systems, so that the states of all the agents can converge to a common value in [25] and [26]. An adaptive distributed affine formation protocol is developed for formation systems, and the constraints in formation operation and the complexity of formation controllers are solved according to the protocol in [27] and [28]. In nonaffine consensus control [29]- [31], the uncertainties in the system are solved in the adaptive framework, thus the system is stable.…”

An Efficient Hierarchical Identification Method With Kernel-Based SVM for Equivalent Systems of Aircrafts

“…Many flight test researches have proved that the LOES models can be used to analyze flying qualities for an un-augmented aircraft with classical dynamic response [1]- [3], which is in reality of high order and nonlinear especially for modern fighters. In addition, the LOES model provides information on the order of state space model and initial values of some aerodynamic derivatives, so the LOES model is an important intermediate result for flight mechanics characterization studies [4]- [6]. The The associate editor coordinating the review of this manuscript and approving it for publication was Dong Shen.…”