1. To solve the problem of GPC huge computation, algorithm with input increment constraints is presented in which the concept of output softness was used to soften the input increments．As a result, the constraints are simplified to be the only one constraint on the current control increment which can be computed directly. At the same time, it needn’t computing the inverse matrix and thus reduces large computation. Moreover, it guarantees the feasibility of the algorithm and has good control performance． 2. To overcome the difficulty in the choice of tuning parameters in traditional GPC, a GPC algorithm with variable parameter design based on BP neural network. is presented，in which the input softness parameters are tuned on line. 3. In this paper, we Identify system by using the least square method with forgetting factor. However, after system simulation, we realize that this method doesn’t fit the Hénon chaotic system perfectly. So we recommend modify this method by other Optimizati

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