Shuffled Frog Leaping Algorithm Research Based Optimal Iterative Learning Control

TL;DR: An optimal ILC algorithm to cope with input constr aint of linear system and nonlinear system and an effective combing optimization technique with iterative learning control is proposed.

Abstract: To solve the problems of nonlinear and input constraints in the iterative learning control system, using real-coded shuffled frog leaping algorithm to solve optimization problem1 in iterative learning control, .A shuffled frog leaping algorithm(SFLA) based optimal iterative learning control is proposed. The algorithm combines the advantages of memetic algorithm and particle swarm optimization to simplify the algorithm of parameter selection, reduce the search space and improve the convergence rate. The proposed approach benefits from the design of a low-pass FIR filter. This filer successfully removes unwanted high frequency components of the input signal, which are generated by SFLA algorithm method due to the random nature of SFLA algorithm search. Simulation are used to illustrate the performance of this new approach, and they demonstrate good results in terms of convergence speed and tracking of the reference signal. INTRODUCTION In automation industry we are facing with systems t-hat perform a certain task over a finite time duration. A sensible example of such systems is a robot manipulator which need to repeat a same tas k over a limited and constant time interval with a high precision. Iterative Learning Control (ILC) [1] is a successful and effective approach for the system above. Improvement of the efficiency is always the seeking target by people for ILC. An effective approa ch combing optimization technique with iterative learning control, which can improve the learning e fficiency of algorithm. Amann, Owens et al. (1996) put forward a more advance approach which is c alled norm-optimal iterative learning control (NOILC) method. Owens, Fang et al. proposed another Parameter optimal iterative learning control (POILC). NOILC and POILC can be applied into linear system easily.It is necessary to design a new method to cope with nonlinear system. As the input var iables are always constrained, it need an algorithms to deal with constrained problem. Hatzikos and Owens designed a new method called genetic algorithm optimal ILC (GA-ILC) , this new method had a good control result. In order to improve the convergence properties of iterati ve learning algorithm, improve shuffled frog leaping algorithm (SFLA) which is applied into all kin ds of optimization problem. This paper proposed an optimal ILC algorithm to cope with input constr aint of linear system and nonlinear system. ILC problem description Considering the linear discrete system model ( 1) ( ) ( ) ( ) ( ) k k k k k x t Ax t Bu t y t Cx t + = + = (1) where k is iteration number. This system is a multi-input and multi-output system. ( ) p k x t R ∈ , ( ) m k u t R ∈ , ( ) n k y t R ∈ are state vector, control vector and output vector of the system respectively. International Conference on Advances in Mechanical Engineering and Industrial Informatics (AMEII 2015) © 2015. The authors Published by Atlantis Press 854 p p A R × ∈ , p m B R × ∈ , n p C R × ∈ are all real matrices. t is the time variable on [0, ] T . Iterative learning control is to seek learning algorithms which can revise the input ( ) k u t constant ly by learning the given reference output ( ) d y t , make the actual output ( ) k y t inching closer to the r eference output ( ) d y t until it can achieve an almost perfect tracking performance. Write controlled plant is the first step of norm-optimal iterative learning control 0 y Pu d = + (2) where P is the plant in question. u U ∈ , 0 , y d Y ∈ .U and Y is the input and output space.U andY are defined as real Hilbert space. The vector form of the input, actual output and reference output can be written as [ (0) (1) ( 1)] T T T T u u u u N = −  , [ (1) (2) ( )] T T T T y y y y N =  , [ (1) (2) ( )] T T T T d d d d y y y y N =  (3) It can get the Markov parameter directly from (1), this parameter can be acquired by the impulse r-esponse of the system easily. The Markov parameter P is 1 i i p CA B − = , 1