MATLAB Implementation of Robust Controller Design

In this paper, we investigate methods for robust controller design. We implement RBF networks to approximate arbitrary nonlinear relationships and apply them to nonlinear PCA modeling. Our primary objective is to minimize the sum of squared errors, which aligns perfectly with the goals of nonlinear PCA. To achieve nonlinear forward and inverse transformations, we employ two distinct RBF networks. Both networks feature three-layer feedforward architectures with radial basis functions serving as activation functions in their hidden layers. The first RBF network performs dimensionality reduction by mapping high-dimensional data to a low-dimensional space (as shown in Figure 4). In MATLAB implementation, this typically involves defining the network structure using `newrb` or `newrbe` functions, setting appropriate spread parameters for Gaussian functions, and training with high-dimensional input data. The second RBF network handles data reconstruction by mapping the low-dimensional outputs back to the original high-dimensional space (Figure 5). This requires separate training with paired low-dimensional inputs and corresponding high-dimensional target outputs. Crucially, both networks must undergo independent training processes to ensure they accurately perform their designated functions. The training algorithm typically involves iterative weight optimization using least-squares methods or gradient descent approaches, with careful consideration of regularization parameters to prevent overfitting. The implementation requires proper data normalization and validation techniques to maintain robustness across different operating conditions.