The linear-quadratic optimal regulator for descriptor systems: discrete-time case
Automatica (Journal of IFAC)
Optimal estimation theory for dynamic systems with set membership uncertainty: an overview
Automatica (Journal of IFAC)
Dynamic Programming and Partial Differential Equations
Dynamic Programming and Partial Differential Equations
Brief Risk-sensitive filtering, prediction and smoothing for discrete-time singular systems
Automatica (Journal of IFAC)
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This paper presents a state estimation approach for an uncertain linear equation with a non-invertible operator in Hilbert space. The approach addresses linear equations with uncertain deterministic input and noise in the measurements, which belong to a given convex closed bounded set. A new notion of a minimax observable subspace is introduced. By means of the presented approach, new equations describing the dynamics of a minimax recursive estimator for discrete-time non-causal differential-algebraic equations (DAEs) are presented. For the case of regular DAEs it is proved that the estimator's equation coincides with the equation describing the seminal Kalman filter. The properties of the estimator are illustrated by a numerical example.