Grey-box System Identification with Variable- Structure Neural Networks

Grey-box’ models take advantage of physical insight about the dynamical system in question. This reduces uncertainty and facilitates the remaining system identification process. Here a grey-box system identification (GBSI) method for nonlinear dynamical systems is presented, which first establishes a linear model (the ‘white box’) using a priori knowledge and conventional tools, and then adds a neural network (the ‘black box’) for learning the residual nonlinear dynamics. What distinguishes this from other GBSI methods is the Variable Structure Learning algorithm, which trains both the neural network connection weights and structure, i.e. number of hidden neurons. The method is tested with two different neural networks using a nonlinear reference function and a realistic aircraft model. INTRODUCTION System identification (SI) refers to the design of a sufficiently accurate model of dynamical systems. ‘Grey-box’ system identification (GBSI) takes advantage of physical insight about the dynamical system in question, for example the model structure and/or certain parameter values. This reduces uncertainty and facilitates identifying the residual, unknown dynamics. Here a nonlinear GBSI method is proposed, which first establishes a linear model (the ‘white box’) using a priori knowledge and conventional tools, and then synergetically adds an artificial neural network, or ANN (the ‘black box’), for learning the residual nonlinear and possibly unmodelled linear dynamics. What distinguishes this from other GBSI methods, for example [1][5][8][12], is the Variable Structure Learning algorithm, which not only trains the ANN connection weights but also the network structure, i.e. number of hidden neurons [9]. The method is tested with two different ANNs using a nonlinear reference function and a high-performance aircraft model. The GBSI process involves three steps: • Create a linear time-invariant model (structure and parameters) based on available a priori knowledge. • Identify the unknown model parameters using conventional linear SI methods and tools. • Train an ANN (weights and structure) to model the residuals dynamics.