High-order state feedback gain sensitivity calculations using computational differentiation

A nonlinear feedback control strategy is presented where the feedback control is augmented with feedback gain sensitivity partial derivatives for handling model uncertainties. Derivative enhanced optimal feedback control is shown to be robust to large changes in the model parameters. The OCEA (Object Oriented Coordinate Embedding) computational differentiation toolbox is used for automatically generating first- through fourth-order partial derivatives for the feedback gain differential equation. Both linear and nonlinear scalar applications are presented. The model sensitivities are obtained about a nominal reference state by defining the Riccati differential equation as being derivative enhanced: OCEA then automatically generates the first- through fourth-order Riccati gain gradients. An estimator is assumed to be available for predicting the model parameter changes. The optimal gain is then computed as a Taylor series expansion in the Riccati gain as a function of the system model parameters. The pre-calculation of the sensitivity gains eliminates the need for gain scheduling for handling model parameter changes. Examples are presented that demonstrate the impact of nonlinear response behaviors, as well as the effectiveness of the generalized sensitivity enhanced feedback control strategy.

High-order state feedback gain sensitivity calculations using computational differentiation Conference Paper