Abstract
This chapter gives a concise description of effective solutions to the guaranteed state estimation problems for dynamic systems with uncertain items being unknown but bounded. It indicates a rigorous theory for these problems based on the notion of evolution equations of the “funnel” type which could be further transformed, through exact ellipsoidal representations, into algorithmic procedures that allow effective simulation, particularly with computer graphics. The estimation problem is also interpreted as a problem of tracking a partially known system under incomplete measurements.
Mathematically, the technique described in this chapter is based on a theory of set-valued evolution equations with the ellipsoidal-valued functions formulating approximation of solutions in terms of set-valued calculus.
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Filippova, T.F., Kurzhanski, A.B., Sugimoto, K., Vályi, I. (1996). Ellipsoidal State Estimation for Uncertain Dynamical Systems. In: Milanese, M., Norton, J., Piet-Lahanier, H., Walter, É. (eds) Bounding Approaches to System Identification. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9545-5_14
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DOI: https://doi.org/10.1007/978-1-4757-9545-5_14
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