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Memory-Based Learning Control

A challenge for learning control systems is to build a model of a nonlinear plant from samples of the plant's inputs and outputs. We have used a memory-based technique to approach this problem. Samples of the plant's inputs and outputs are stored in a memory. Predictions of the plant's outputs given an input vector (or vice versa) are made by constructing a local model from nearby samples, and using the local model to interpolate between and extrapolate from samples in the database. This approach implements a philosophy of modeling a complex plant with many simple local models. A local model is constructed by performing a regression of a polynomial surface on the data. The regression is locally weighted by a weighting function of the distance between the desired vector and each vector stored in memory. In order to find relevant information in the memory and to perform the locally weighted regression a distance metric, weight function shape parameter, and ridge regression parameters are required. These parameters are found using a cross-validation approach. The parameters indicate which variables and terms in the local model are relevant to modeling the plant.