A PD-Type Iterative Learning Algorithm for Semi-Linear Distributed Parameter Systems with Sensors/Actuators

Abstract

In this paper, the control problem of semi-linear distributed parameter system (DPS) with sensors/actuators is considered using iterative learning control (ILC) method. During the learning process, the output signals of the system exist random data dropout which is described as a Bernoulli random variable. Then, a novel intermittent updating PD-Type ILC algorithm is proposed on the basis of the available output information. In this kind ILC algorithm, the scheme only updates its control signal when the output signal is successfully transmitted. Hence, the intermittent updating PD-Type ILC algorithm is presented for a semi-linear parabolic DPS based on single sensor and single actuator, and the convergence condition of the output error is obtained by using Bellman-Gronwall lemma and semigroup theory under some given assumptions. Secondly, this kind PD-Type ILC law is extended to control the semi-linear DPS with multiple sensors and multiple actuators. Lastly, one example is given to demonstrate the effectiveness of the proposed scheme.