Optimal estimation of the time instant of occurrence of an impulse disturbance in a random signal in discrete time

1993 ◽  
Vol 36 (6) ◽  
pp. 317-324 ◽  
Author(s):  
A. V. Vanzha ◽  
A. A. Maltsev ◽  
A. M. Silaev
Keyword(s):  
Discrete Time ◽  
Optimal Estimation ◽  
Time Instant ◽  
Random Signal

Finite-time optimal control of a process leaving an interval

1996 ◽  
Vol 33 (03) ◽  
pp. 714-728
Author(s):  
Douglas W. Mcbeth ◽  
Ananda P. N. Weerasinghe
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Finite Time ◽  
Simple Random Walk ◽  
Time Instant ◽  
Initial Position ◽  
Time Problem ◽  
Control Set ◽  
Playing Time ◽  
Variance Parameters

Consider the optimal control problem of leaving an interval (– a, a) in a limited playing time. In the discrete-time problem, a is a positive integer and the player's position is given by a simple random walk on the integers with initial position x. At each time instant, the player chooses a coin from a control set where the probability of returning heads depends on the current position and the remaining amount of playing time, and the player is betting a unit value on the toss of the coin: heads returning +1 and tails − 1. We discuss the optimal strategy for this discrete-time game. In the continuous-time problem the player chooses infinitesimal mean and infinitesimal variance parameters from a control set which may depend upon the player's position. The problem is to find optimal mean and variance parameters that maximize the probability of leaving the interval [— a, a] within a finite time T > 0.

Finite-time optimal control of a process leaving an interval

1996 ◽  
Vol 33 (3) ◽  
pp. 714-728 ◽  
Author(s):  
Douglas W. Mcbeth ◽  
Ananda P. N. Weerasinghe
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Finite Time ◽  
Simple Random Walk ◽  
Time Instant ◽  
Initial Position ◽  
Time Problem ◽  
Control Set ◽  
Playing Time ◽  
Variance Parameters

Consider the optimal control problem of leaving an interval (– a, a) in a limited playing time. In the discrete-time problem, a is a positive integer and the player's position is given by a simple random walk on the integers with initial position x. At each time instant, the player chooses a coin from a control set where the probability of returning heads depends on the current position and the remaining amount of playing time, and the player is betting a unit value on the toss of the coin: heads returning +1 and tails − 1. We discuss the optimal strategy for this discrete-time game. In the continuous-time problem the player chooses infinitesimal mean and infinitesimal variance parameters from a control set which may depend upon the player's position. The problem is to find optimal mean and variance parameters that maximize the probability of leaving the interval [— a, a] within a finite time T > 0.

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