On the asymptotic behavior of sensors' allocation algorithm in stochastic distributed systems

In a recent paper (see Int. J. Control, vol.22, p.197-214 (1975)), an algorithm is presented for the optimal simultaneous allocation of a finite number of sensors in a stochastic distributed parameter system. When applying the algorithm recursively on a time-invariant system, two important questions arise for the resulting time-variant Riccati equation. First, the existence of a steady-state solution, i.e. the determination of conditions to be satisfied for such a solution to exist. Secondly, the stability of the algorithm, i.e. does the effect of initial errors become negligible as time evolves. These two questions are investigated. First, the existence of a steady-state optimal solution is demonstrated, the necessary conditions for the convergence of the algorithm towards this optimal solution are then discussed.