Iterative learning control for fractional-order multi-agent systems

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.…”

“…From (25) and (27) the error of input δu k+1 (t) is rewritten in the following compact form by (13) and 14:…”

Consensus Tracking Via Iterative Learning Control for Singular Fractional-Order Multi-Agent Systems Under Iteration-Varying Topologies and Initial State Errors

“…Iterative learning control (ILC) has been widely utilized to cope with the repeated tracking control with high precision requirement in the fixed time interval due to its simplicity and effectiveness [8], [9]. Hence, ILC has been successfully implemented to many kinds of multi-agent systems in recent references, such as high-order nonlinear MASs [10], singular MASs [11], fractional-order MASs [12], and distributed parameter MASs [13]- [15], etc.. In [16], [17], the formation control problems of nonlinear MASs under switching interaction topologies were addressed by employing the ILC scheme.…”

“…Meanwhile, the consensus control of factional-order MASs have been widely concerned from different aspects [30]- [32]. Based on the memory property of fractional-order derivative, the D αtype and P I β -type iterative learning control protocols were applied to handle consensus tacking for nonlinear fractionalorder MASs with fixed and iteration-varying communicating graphs, respectively [12], [32].…”

Convergence analysis for iterative learning control of conformable fractional differential equations

“…Since Uchiyama 13 and Arimoto and Kawamura 14 offered to use the idea of iterative learning strategy to track a desired trajectory, various version iterative updating laws are proposed for different type dynamical systems (see, for example, previous studies [15][16][17][18][19][20][21]. Recently, Wang et al 22 proposed conformable D -type learning updating law to study iterative learning control for the linear conformable fractional differential equations and established a new convergence result; however, there exists quite a few study on iterative learning control for nonlinear conformable fractional differential equations via P-type and D -type iterative updating laws.…”