Accelerated Convergence of Neural Network System Identification Algorithms via Principal Component Analysis

While significant theoretical and experimental progress has been made in the development of neural networkbased systems for the autonomous identification and control of space platforms, there remain important unresolved issues associated with the reliable prediction of convergence speed and the avoidance of inordinately slow convergence. Focusing here on autonomous identification of lightly damped space structures, we first show that even apparently benign and simple examples can exhibit unpredictably slow convergence when the standard Least Mean-Square (LMS)-style identification algorithms are applied. To speed convergence of neural identifiers, we introduce the preprocessing of identifier inputs using Principal Component Analysis (PCA) algorithms. PCA is a procedure (that is realizable via a neural network) for the automatic generation of a transformation of the neural identifier's external inputs that makes the correlation matrix identity. When inputs are pre-processed in this way, enormous improvements in the convergence speed of the neural identifier is obtained. From a study of several such algorithms, we developed a new PCA approach which exhibits excellent convergence properties, insensitivity to noise and reliable accuracy. Numerical examples show many orders of magnitude reduction in the time required for convergence of system identifiers.