This dissertation develops a method of control for nonlinear processes based on regression trees with kernel regression at the leaves as a general control methodology. This methodology offers the ability to control a wide variety of processes exhibiting nonlinear behavior. It takes a place with other machine learning methods that are being applied to nonlinear control, but it does not suffer from the shortcomings of other methods. The method draws on two well-known machine learning methods, regression trees and kernel regression. This dissertation shows that this control method may be programmed from supervised runs of a process and it may be updated from follow-on runs. The method may serve as a backup controller for redundancy or it may be the primary controller for a process after supervised training by an expert operator.

Model trees are a generalized form of regression tree where the leaves contain more than one data point and a small kernel regression is performed when a leaf is selected by navigation through the tree. Kernel regression is a form of instance-based learning where the prediction is formed by distance-weighted input of the data. Kernel regression has been shown to fit complex, nonlinear forms quite well, but it suffers from scalability to higher dimensions as a potential control method. Using kernel regression with the innovative approach of constructing the model tree in a way to create a predicted control setting is the contribution of this research to the area of nonlinear control.

During this dissertation, the performance of model trees for situations of nonlinear control was demonstrated in four widely-varying settings. In all cases, the model tree was developed from process data in a common form. Where data were available to both develop the model tree and compare its prediction to retained test data, the model tree was able to demonstrate control prediction. Statistical tests of hypotheses failed to reject a null hypothesis of equal means and variances. Where the model tree could be created from a simulation and then used as a predictive control, the results demonstrated that the model tree could be used as a controller to meet process goals.

The demonstrations in this research displayed many different forms of nonlinearity that may be encountered in processes. In addition to typical nonlinear factors such as power equations and trigonometric functions, these demonstrations exposed the model tree to sudden, non-deterministic inputs and changes to inputs. Inputs that represent integer multiples of power sources are experienced. In some processes, the system includes some regions of linear response, but the boundaries of a region have a sudden change of slope or even an inflection point. Model trees with kernel regression at the leaves demonstrated the ability to handle these scenarios.