Risk sensitive identification of linear stochastic systems (Q2576701)

This paper extends the idea of risk-sensitive identification of Gaussian AR-processes first considered by \textit{A. Stoorvogel} and \textit{J. H. van Schuppen} [System identification with information theoretic criteria. NATO ASI Ser., Ser. F, Comput. Syst. Sci. 153, 289--338 (1996; Zbl 1065.93508)] to ARMA-processes and multi-variable linear stochastic systems by formulating a new risk sensitive identification criterion \(J(K)\) with a fixed weighting matrix \(K\) in recursive identification procedure. First a feasible set \(E_K\) is defined, where the cost function \(J(K)\) is well-defined and finite. Based on the expression of the criterion given in LEQG (Linear Exponential Quadratic Gaussian)-theory, it is shown that \(J(K)\) has a unique stationary point in \(E_K\), and that the stationary point is first determined for an extended, relaxed matrix-valued constrained minimization problem, where the equality constraints are defined by a control-Riccati equation. Then, it is proved by using a filter-Riccati representation of \(J(K)\), that the stationary point is the unique minimum of \(J(K)\) over \(E_K\). Furthermore, it is shown that the unique minimum is also minimizing \(J(K)\) over \(E_K^o\), a slightly larger set.