The original iterative learning control (ILC) algorithm is a control algorithm to make the output approach a set objective, where the control input is learned from and corrected by the error of repeatedly tracking the given objective. Since it was proposed by Uchiyama and Arimoto in the 1970s and 1980s, ILC has become a powerful tool for solving the model-free control problems by applying the periodic and repetitive learning process. However, the original ILC is designed for the same system to track the same goal from the same initial condition. The strict requirement for repeatability limits the application range of the original ILC.
For example, generic information will be generated by the operation from a series of systems with the same structure and similar parameters (SysSP). Meanwhile, the generic information is inadequately applied in original ILC due to its strict limitations in repeatability, which affects the overall efficiency of ILC for SysSP. Therefore, this paper proposes a cooperate ILC algorithm to solve the problem.
Firstly, for a single-input-single-output-single-state SysSP, a state-space model with the property of parameter perturbation is established is established, the goal of the control is set, subsequently a mathematical description is formed. Then, inspired by the learning and recognition process, the ideology of ILC for SysSP is formulated and algorithm of ILC for SysSP is established： the law of cooperate learning is formed based on the feature where the commonalities and common cognition are formed from optimizing by repetitively learning and summarizing from the predecessors; the differences in the parameters of the different systems are ignored in the cooperate learning law and the algorithm is proceed by a fixed time sequence to obtain a convergent cooperate control input with commonalities; the control strategy initialized with the cooperate control input is developed, on the basis of the feature that the descendant will construct their cognition based on not only the fixed, precise commonalities by the predecessors but also the surrounding environment and individual requirement. Finally, simulations and validations are conducted for ILC for the selected 5 SysSPs. The control efficiencies of original ILC and the ILC for SysSP are analyzed based on the total number of the iterations under the two algorithms.
Case simulation demonstrate that： under the random initial control input, the control input converges to the cooperate control input after 64 periods of iteration, after which the maximum absolute error in the output is less than 1.5×10-4 after 174 cycles or about 867 times of iteration (there are 5 times of iterations in a fully operated cycle), while it takes 331 cycles or 1 655 times of iterations to bring the error to the same level when original ILC is applied with the same parameter. For a given system, the error is 0.003 4 in the first iteration when the cooperate control input is applied, which is much less than the initial error when the original ILC applied; the error will converge into 0.000 15 after 79 times of cooperate iteration, while it takes 330 times of original iteration. The difference between the outputs by applying the two algorithms is of the order of 10-19 when the algorithms converge, showing that the cooperate iteration has no effect on the accuracy of the output.
Therefore, a more general conclusion can be drawn that： compared with original ILC, cooperate ILC will be of a higher efficiency without loss of accuracy. A reduced number of iterations will be observed by taking the cooperate control input as the initial value of the control input.
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