Sensitivity Analysis for Systems of Differential-Algebraic Equations with Applications to Predictive Control and Parameter Estimation

Systems of differential-algebraic equations (DAEs) are a natural description for mathematical models of many real-life processes consisting of the interconnection of different physical components with their own dynamic behavior. Such interconnected systems can be described by separate subsystem models, for instance related to electric drives and mechanical components in power trains. Interface conditions are used to connect these subsystems by a description of power flow or, for example, geometric side conditions imposed by links or joints. In this paper, procedures for the computation of state sensitivities with respect to parameters and control inputs are described for DAE formulations of control applications. Procedures for sensitivity analysis are used to investigate the performance of control systems and to derive novel predictive control approaches aiming at accurate trajectory tracking and rejection of external disturbances, as well as procedures for state and parameter estimation.