State Observer-Based Iterative Learning Control of an Uncertain Continuous-Time System

Robust iterative learning control for uncertain continuous‐time system with input delay and random iteration‐varying uncertainties

“…Therefore, following [52,60]) (see also Remark 2), to model the above system in a multiplicative uncertain form (9), W a should be chosen such that ( j )e − ĵ| for 1000 random samples of parameters uncertainties. As can be seen from Figure 9, the chosen W a is suitable.…”

“…Therefore, following [52,60]) (see also Remark 2), to model the above system in a multiplicative uncertain form (9), W a should be chosen such that Figure 10 shows the magnitude plot of Υ a and Υ b with respect to the frequency. Now, both boundedness and convergence of both expectation and variance of the tracking error are guaranteed as k → ∞.…”

“…We also refer readers to [7] for a survey on the synthesis and convergence analysis of stochastic ILC. Because uncertainties are inevitable, especially in engineering applications, several ILC methods have been presented in the area of uncertain systems, for example, see [8][9][10][11]. However, the ILC designs in [8][9][10][11] depend on the assumption that some factors such as reference trajectory, initial conditions and disturbances should be strictly iteration-invariant, which does not match the 'practical nature' of ILC [12].…”

“…Because uncertainties are inevitable, especially in engineering applications, several ILC methods have been presented in the area of uncertain systems, for example, see [8][9][10][11]. However, the ILC designs in [8][9][10][11] depend on the assumption that some factors such as reference trajectory, initial conditions and disturbances should be strictly iteration-invariant, which does not match the 'practical nature' of ILC [12]. Therefore, over the past years, many studies have been devoted to deal with the issue of iteration-varying (nonrepetitive) uncertainties in ILC designs, for example, see [12][13][14][15][16][17][18][19][20].…”