Sensitivity Analysis for Reliable Feedforward and Feedback Control of Dynamical Systems with Uncertainties

In many applications in control engineering, accurate feedforward control strategies have to be developed which aim at tracking of desired state or output trajectories. For differentially flat dynamic systems, this task is usually solved analytically by symbolic formula manipulation which is supported by software tools like MAPLE. However, these analytic approaches fail in cases for which exact solutions are not available. Such situations occur either if the initial states of the dynamic process are not consistent with the desired state and output trajectories or if significant parameter uncertainties exist. In both scenarios, control strategies can be derived on the basis of a sensitivity analysis of the process model under consideration. In this procedure, the sensitivity analysis is applied to a suitable performance criterion describing the tracking accuracy of the desired state and output trajectories. In this paper, we give an overview of basic sensitivity-based control techniques. Moreover, we extend them to uncertain process models in which both tolerances of the parameters of the plant to be controlled and measurement uncertainties are represented directly by corresponding intervals. Finally, we present a novel sensitivity-based control procedure making use of interval arithmetic approaches and apply it to an example highlighting its practical applicability.