PD^α‐type distributed learning control for nonlinear fractional‐order multiagent systems

Abstract

This paper considers the consensus tacking problem for nonlinear fractional-order multiagent systems by presenting a PD -type iterative learning control update law with initial learning mechanisms. The asymptotical convergence of the proposed distributed learning algorithm is strictly proved by using the properties of fractional calculus. A sufficient condition is derived to guarantee the whole multiagent system achieving an asymptotic output consensus.An illustrative example is given to verify the theoretical results. KEYWORDS asymptotical convergence, nonlinear fractional-order multiagent systems, PD -type iterative learning control Math Meth Appl Sci. 2019;42:4543-4553.wileyonlinelibrary.com/journal/mma

Consensus tracking problem for linear fractional multi-agent systems with initial state error

“…In other words, the distributed error η k,i (t) rather than e k,i (t) is used in the following algorithms. The other reason is that we require a suitable causality between the input and tracking error according to (1) so that the input signals can be updated effectively [13,14]. In other words, it is the suitable derivation of the distributed error rather than itself will be employed.…”

Fractional-Order Iterative Learning Control with Initial State Learning for a Class of Multiagent Systems

“…In the same year, Cao and Ren [6] also applied the consensus theory to the formation control problem of FOMASs. Since then, the research and application of FOMASs consensus problems have been emerging, including linear fractional-order multiagents [7][8][9][10] and nonlinear fractional-order multiagents [11][12][13][14]. Song and Cao [7] used the stability theory of FOSs and linear matrix inequality to study the consensus problem of linear FOMASs.…”

“…Similarly, in [10,11], the adaptive control and the sampling data control were designed to solve the consensus problem of nonlinear and linear FOMASs with and without leader-following structure, and some sufficient and necessary conditions related to fractional order, coupling gain, and Laplacian matrix spectrum were obtained to ensure that the system can achieve consensus. For the study of nonlinear FOMASs, there are also literatures [12][13][14].…”

Preview tracking control for a class of fractional-order linear systems

“…Reference [8] investigates the existence, uniqueness and Hölder continuity of solutions to the time-fractional Navier-Stokes equations. In recent years, the study of fractional-order systems has been extended to the field of robust control, optimal control, sliding mode control, fault-tolerant control, iterative learning control and other advanced control strategies [9][10][11][12][13][14][15][16][17][18]. Reference [9] studies the static output feedback control problem of fractional uncertain systems by using the linear matrix inequality method.…”

“…Based on the properties of fractional derivative and generalized Gronwall inequality, a P-type iterative learning control updating laws for a class of delay fractionalorder systems is given in [15]. In [16], a PD α -type distributed iterative learning control laws is proposed for consensus tracking of nonlinear fractional multi-agent systems. Reference [17] discusses the problem of complete tracking for a class of fractional-order systems in a finite-time interval, and gives fractional-order iterative learning control laws involving a local average operator associated with probability.…”