State estimation for dynamical system described by linear equation with uncertainty

TL;DR

This paper develops explicit minimax estimation methods for linear dynamical systems with uncertain parameters in Hilbert space, providing solutions for both abstract equations and specific descriptor differential equations.

Contribution

It introduces explicit formulas for minimax state estimation under quadratic uncertainty sets in Hilbert spaces, extending to descriptor differential equations.

Findings

Explicit minimax estimation formulas derived

Error bounds established for uncertain parameters

Application to descriptor differential equations demonstrated

Abstract

In this paper we investigate a problem of state estimation for the dynamical system described by the linear operator equation with unknown parameters in Hilbert space. We present explicit expressions for linear minimax estimation and error provided that any pair of uncertain parameters belongs to the quadratic bounding set. As an application of the main result we present the solution of minimax estimation problem for the linear descriptor differential equation with constant matrices.