Real time adaptive PID controller based on quantum neural network for nonlinear systems

In this paper, an adaptive proportional-integral-derivative (PID) controller based on a quantum neural network (APIDC-QNN) is introduced. In the proposed neural network structure, three neural layers are used namely: input layer, hidden layer, and output layer. The input and hidden layers use three and six quantum-processing neurons respectively. In contrast, in the output layer, the multiplication processing is used as an activation function free of the output weights which aims to reduce the number of tunable parameters. The output layer with three neurons represents the adaptive PID controller parameters. In this work, the tunable parameters are updated using the Lyapunov stability criterion to guarantee optimization and learning stability. In addition, the plant identification based on the Wiener-type model and quantum neural network is introduced to estimate the sensitivity of the plant output to the control signal. The proposed neural network structure yields only 30 tunable parameters for the proposed controller and 13 tunable parameters for the proposed identifier while the conventional neural network structure in other works requires 90 tunable parameters just for the controller. To evaluate the performance of the proposed APIDC-QNN, it is practically operated on a non-holonomic two-wheel mobile robot (NHWMR). Moreover, to investigate the robustness, superiority, and convergence speed of the proposed APIDC-QNN, some experimental tasks are discussed. The simulation and practical results show the powerful processing and the superiority of the proposed APIDC-QNN over that designed based on conventional neural networks by recording the minimum values of the performance indices.