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Chaos Control of Vibro-impact System with Soft Constraint Based on RNN

For the chaotic motion control of a single-degree-of-freedom vibro-impact system with soft constraint, a parameter-feedback chaos control method based on ridgelet neural network (or RNN for short) is proposed. The parameter feedback chaos controller is designed based on RNN, and the output energy of the controller and the distance between two adjacent points on the Poincare cross section was used as the weighted terms to construct a fitness function, so as to guide the adaptive multiple sub-population collaboration QPSO algorithm (or AMPCQSO for short) to optimize the parameters of the controller. The controller optimized is used to output a small perturbation to adjust the damping coefficient of the system, thus the chaotic motion can be controlled to the desired periodic motion. In the proposed method, the design of the controller does not depend on the precise mathematical model of the controlled system, so this method is suitable for the case where the precise mathematical model of the controlled system is unknown and only the input/output data can be obtained. In the simulation experiment, the influence of the number of hidden layer nodes in RNN on chaos control effect is further analyzed and studied. The simulation results show that the expected control target can be achieved when there are 5 or 6 hidden layer nodes of RNN, but When the number of hidden layer nodes is 5, the structure of RNN is simpler and the optimized speed of controller parameters is faster.