Sensitivity Methods for Analysis and Design of Dynamic Systems with Applications in Control Engineering

In this work, a unified approach is presented for the sensitivity analysis of dynamic systems and for the use of sensitivity values in selected applications from the field of control engineering. These applications highlight how sensitivity-based procedures can be employed for designing novel robust and efficient feedforward and feedback control techniques as well as state and parameter estimation approaches. Moreover, optimization and identification tasks can be handled within the same framework.

In this context, differential sensitivities represent partial derivatives of the state trajectories of a discrete-time or continuous-time dynamic system with respect to at least one of the following quantities, namely, initial conditions of the state vectors, system parameters, control inputs, and disturbance variables.

Using software libraries for algorithmic differentiation, differential sensitivities can be computed for dynamic system models that are either stated as ordinary differential equations, differential-algebraic equations, partial differential equations, or finite-dimensional sets of difference equations. With the help of the computed differential sensitivities, small-signal information can be determined concerning the influence of the above-mentioned quantities on the state trajectories. Besides the use of classical floating point arithmetic, interval arithmetic is made use of when worst-case bounds of selected uncertain parameters are known during design, simulation, and verification stages.