Neural Networks in Control Applications

The intention of this report is to make a systematic examination of the possibilities of applying neural networks in those technical areas, which are familiar to a control engineer. In other words, the potential of neural networks in control applications is given higher priority than a detailed study of the networks themselves. With this end in view the following restrictions have been made: - Amongst numerous neural network structures, only the Multi Layer Perceptron (a feed-forward network) is applied. - Amongst numerous training algorithms, only four algorithms are examined, all in a recursive form (sample updating). The simplest is the Back Probagation Error Algorithm, and the most complex is the recursive Prediction Error Method using a Gauss-Newton search direction. - Over-fitting is often considered to be a serious problem when training neural networks. This problem is specifically examined, and it appears that considering 'normal' neural network models with, say, 500 samples, the problem of over-fitting is neglible, and therefore it is not taken into consideration afterwards. Numerous model types, often met in control applications, are implemented as neural network models are examined. The models are separated into three groups representing input/output descriptions as well as state space descriptions: - Models, where all in- and outputs are measurable (static networks). - Models, where some inputs are non-measurable (recurrent networks). - Models, where some in- and some outputs are non-measurable (recurrent networks with incomplete state information). The three groups are ordered in increasing complexity, and for each group it is shown how to solve the problems concerning training and application of the specific model type. Of particular interest are the model types concerning canonical, observable state space forms (minimum realizable form) for SISO as wll as MIMO processes. The tests show that all models, after succeeeful training, which is judged by correlation analysis of the prediction errors, are able to perform non-linear system identification, prediction, simulation and filtering of dynamic, non-linear, multi-variable and noisy processes in a very satisfactory manner. The further examinations mainly concentrate on two models, the Non-linear ARMAX (NARMAX) model representing input/output description, and the Non-linear Innovation state Space (NISS) model (a Kalmann filter) representing state space description. The potentials of neural networks for control of non-linear processes are also examined, focusing on three different groups of control concepts, all considered as generalizations of known linear control concepts to handle also non-linear processes. - Control concepts including parameter estimation - Control concepts including inverse modelling - Control concepts including optimal control For each of the three groups, different control concepts and specific training methods are detailed described.Further, all control concepts are tested on the same simulated process and compared. The closing chapter describes some practical experiments, where the different control concepts and training methods are tested on the same practical process operating in very noisy environments. All tests confirm that neural networks also have the potential to be trained to perform excellent control of dynamic, non-linear, multi-variable and noisy processes.