Optimal observation problems accompanying measurement optimal control problems

Two classes of optimal observation problems arising in the context of optimal robust control of linear systems under inaccurate and incomplete state measurements are investigated. Linear optimal observation problems are associated with the construction of optimal guaranteed open-loop controls and provide estimates of information sets that describe states consistent with measurements obtained. A priori optimal observation problems are related to the synthesis of multiple-closable control strategies and the determination of the worst-case future information sets. These problems are formulated as specific multi-level mathematical programming problems, for which a recurrent procedure for their reduction to large-scale linear programming problems is developed. The proposed algorithms are oriented towards real-time applications in optimal guaranteed control systems.