Networked Iterative Learning Control Design for Nonlinear Systems with Stochastic Output Packet Dropouts

Abstract

This paper develops two proportional-type (P-type) networked iterative learning control (NILC) schemes for a class of discrete-time nonlinear systems whose stochastic output packet dropouts are modeled as 0-1 Bernoulli stochastic sequences. In constructing the NILC schemes, two kinds of compensation algorithm of the dropped outputs are given. One is to replace the instant-wise dropped output data with the synchronous desired output data; the other is to substitute the dropped data with the consensus-instant output data used at the previous iteration. By adopting the lifting technique, it is derived that under certain conditions the expectations of the tracking errors incurred by the proposed NILC schemes converge to zero along the iteration axis. Numerical experiments are carried out for validity and effectiveness.

Iterative Learning Control for Nonlinear Systems with Data Dropouts at Both Measurement and Actuator Sides

“…From (27) and A4, backward iterating the state difference similarly to (17) we have From (27) and A4, backward iterating the state difference similarly to (17) we have…”

“…Thus, it is apparent that lim k→∞ ‖ u c k (t)‖ ∞ = 0 and lim k→∞ ‖ u r k (t)‖ ∞ = 0. Furthermore, by (17) we know lim k→∞ ‖ x k (t)‖ ∞ = 0 and then lim k→∞ e k (t) = 0, ∀t. This completes the proof.…”

“…For example, unmanned aerial vehicles (UAVs) can be used for surveillance of some specified area and the surveillance routine is usually repeatable. Several papers have been dedicated to the design and analysis of ILC algorithm under random data dropouts environments [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Another similar example is the trajectory-keeping control in satellite formation flying [9].…”

“…The data dropout is assumed to occur only at the measurement side in [12][13][14][15][16][17][18][19][20][21], that is, only the output data might be lost during the transmission from the plant to the controller, while the network from the controller to the plant is assumed to work well. The inherent principle in these papers is that, if the tracking information is successfully transmitted back to the controller, then the algorithm updates its input signal, otherwise the algorithm stops updating and retains its previous signal.…”

“…The inherent principle in these papers is that, if the tracking information is successfully transmitted back to the controller, then the algorithm updates its input signal, otherwise the algorithm stops updating and retains its previous signal. The convergence was established in the mean square sense [12][13][14], mathematical expectation sense [10,[15][16][17], and almost sure sense [18][19][20][21]. Additionally, in [17,20,21], the authors also provided an alternative compensation scheme for the lost measurement, i.e., substituting the dropped packet with the synchronous one from its previous iteration.…”