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Traditional PID neural network adopts BP learning algorithm. However, without accurate gradients, its initial MSE is too large and the procedure of convergence may be unstable. A modified PSO (MPSO) algorithm is introduced to training the PID neural network. The MPSO algorithm does not need any gradient information. It can keep large variety all along and solve premature convergence, which is a major problem in basic PSO algorithm. Simulation results show MPSO algorithm is the best learning algorithm for PID neural network.

In this paper, the proportional (P) neuron, integral (I) neuron and derivative (D) neuron are introduced and a new neural network: PID neural network (PIDNN) is built. Based on the PID neural network, a multivariable system which has 3 inputs and 2 outputs is discussed and the paper displays the perfect performances of the PIDNN for the unsymmetry multivariable system.