Robust Iterative Learning Control of 2-D Linear Discrete FMMII Systems Subject to Iteration-Dependent Uncertainties

Higher‐Order Iterative Learning Control with Optimal Control Gains Based on Evolutionary Algorithm for Nonlinear System

“…For instance, to destroy a target with bombs, the proposed method can reduce the number of bombs at the cost of computing time. Future research will extend the EA-HOILC developed in this paper to the dynamical systems with uncertainties in real application [35][36][37].…”

“…Applying Lemma 1 to (21) with convergence condition (10) and considering (17) and (20), we can derive…”

“…By using the control input and tracking information of previous iterations, the control input signal can be gradually updated from iteration to iteration such that the tracking performance can be improved. Less previous knowledge about the controlled systems makes ILC popular in theoretical fields [9][10][11][12][13][14] as well as applicable fields [15][16][17][18][19].…”

Robust decentralized iterative learning control for large‐scale interconnected systems described by 2‐D Fornasini–Marchesini systems with iteration‐dependent uncertainties including boundary states, disturbances, and reference trajectory

“…In addition, $$$ \left\Vert {\bar{E}}_0(j)\right\Vert $$$ is bounded for $$$ j=0,1,\dots, {T}_2 $$$ due to the boundedness property of $$$ {y}_{n,0}^d\left(i,j\right) $$$ and $$$ {y}_{n,0}\left(i,j\right) $$$. For ()–(), applying lemma 2 in Reference 28, if $$$ \left\Vert {\overline{\Phi}}_7\right\Vert <1 $$$ is satisfied, there is $$$$ \underset{k\to +\infty }{\lim\ \sup}\left\Vert {\bar{E}}_k(j)\right\Vert \le {b}_{\bar{E}},j=1,2,\dots, {T}_2. $$$$ From () and (), for $$$ n=1,2,\dots, N $$$, $$$ i=1,2,\dots, {T}_1 $$$, and $$$ j=1,2,\dots, {T}_2 $$$, we have …”

“…Further, we know that $$$ \left\Vert \delta {x}_k\left(0,j\right)\right\Vert $$$, $$$ \left\Vert \delta {x}_k\left(i,0\right)\right\Vert $$$, $$$ \left\Vert \delta {\overline{X}}_k(0)\right\Vert $$$, $$$ \left\Vert \delta {\overline{W}}_k\left(j-1\right)\right\Vert, \left\Vert \delta {\overline{Y}}_k^d(j)\right\Vert $$$, and $$$ \left\Vert \delta {\overline{V}}_k(j)\right\Vert $$$ are bounded. For ()–(), applying lemma 2 in Reference 28, if $$$ {\tilde{\Psi}}_6=\left\Vert {\overline{\Psi}}_8\right\Vert <1 $$$ is satisfied, there is $$$$ \underset{k\to +\infty }{\lim\ \sup}\left\Vert {\overline{\overline{\zeta}}}_{k+1}\left(j+1\right)\right\Vert \le {b}_{\overline{\overline{\zeta...$$…”