Akio Tanikawa

New Smoothers for Discrete-time Linear Stochastic Systems with Unknown Disturbances

We consider discrete-time linear stochastic systems with unknown disturbances and study the fixed-point smoothing problem for these systems. A new smoothing algorithm which is robust with respect to the unknown disturbances is derived from the optimal filter with disturbance decoupling property for those systems. It is shown that this algorithm reduces to the standard optimal smoother derived from the Kalman filter when the unknown inputs disappear. This indicates that the new smoothing algorithm is a natural extension of the standard optimal smoother to the linear systems possibly with unknown inputs.

On General Conditions for Laws of Large Numbers in Random Linear Programs

Numerical computations of large-scale linear programming problems often contain instability owing to modelling errors and accumulation of round-off errors. The question discussed here is whether the effect of these errors increases or decreases with the size of the problem. It is shown that the random errors in the original data have diminishing effects on the optimum as the number of variables increases. This result is stated in terms of the law of large numbers.