Feedback Control Sensitivity Calculations Using Computational Differentiation

Feedback control is a powerful methodology for handling model and parameter uncertainty in real-world applications. Given a useful nominal plant model for developing the control approach, it is well-known that optimal solutions only perform well for a limited range of model and parameter uncertainty. A higher-order optimal nonlinear feedback control strategy is presented where the feedback control is augmented with feedback gain sensitivity partial derivatives for handling model uncertainties. The computational differentiation (CD) toolbox is used for automatically generating higher-order partial derivatives for the feedback gain differential equations. An estimator is assumed to be available for predicting the model parameter changes. The optimal gain is computed as a Taylor series expansion in the gains, where the feedback gains are expanded as a function of the system model parameters. Derivative enhanced optimal feedback control is shown to be robust to large changes in the model parameters. Numerical examples are presented that demonstrate the effectiveness of the proposed methodology.