Toward the Optimal Parameterization of Interval-Based Variable-Structure State Estimation Procedures ∗

Feedback control strategies for continuous-time dynamic systems rely, on the one hand, on a mathematical system model given as a set of (ordinary) differential equations and, on the other hand, on knowledge about the current state variables and system parameters. However, most practical applications are characterized by the fact that not all state variables are directly measurable and that system parameters are either only imprecisely known or may change their values during system operation. This typically leads to the necessity to determine the before-mentioned non-measurable quantities by means of model-based online estimation procedures, for which a guaranteed asymptotically stable convergence to the true, however, unknown values has to be ensured. In this context, variable-structure state estimation procedures represent powerful approaches because candidates for Lyapunov functions are employed in an underlying manner to perform a proof of the required stability properties. In this paper, a novel interval-based variable-structure state and parameter estimation procedure is presented for which a systematic approach toward an optimal parameterization is presented. The parameterization aims at simultaneously attenuating the influence of (stochastic) noise and maximizing the regions in the state and parameter space for which stability can be proven.