State space representation of the tracking error of the marine vehicle using CEW-WNN-ARX-MM model

The main objective of this paper is to introduce a state space representation of the tracking error of a marine vehicle using a combination of mathematical and statistical models. To this end, a statistical model named cubic exponential weight wavelet network ARX (CEW-WNN-ARX ) model is introduced. The CEW-WNN-ARX model is an ARX model whose coefficients are approximated by a cubic exponential weight wavelet neural network (CEW-WNN). The CEW-WNN is an enhanced type of wavelet neural network comprising of five layers: input, wavelet, product, output and cubic exponential weight layer that computes weights as cubic exponential function of inputs thus allowing them to vary with the inputs and share the dynamics with the wavelet compartment. The CEW-WNN-ARX model possesses both the advantages of the state-dependent ARX model in the description of nonlinear dynamics using few nodes and of the CEW-WNN model in functional approximation considering mutually the time and frequency domains. Firstly, the nonlinear dynamic between the heading angle deviation and the rudder angle of ship is characterized by the CEW-WNN-ARX model, which is later identified by the SNPOM. Then the heading angle deviation is integrated into mathematical model. Finally, the state space representation of tracking error is derived. The effectiveness of the proposed model is shown using the data obtained from the Shioji-maru experimental ship of Tokyo University of Marine Science and Technology of Japan.