Optimal Control of the Observation Process

1996 ◽  
pp. 509-542
Author(s):  
V. N. Afanas’ev ◽  
V. B. Kolmanovskii ◽  
V. R. Nosov
Keyword(s):  
Optimal Control ◽  
Observation Process

scholarly journals Stochastic filtering and optimal control of pure jump Markov processes with noise-free partial observation

2020 ◽  
Vol 26 ◽  
pp. 25
Author(s):  
Alessandro Calvia
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Infinite Horizon ◽  
Value Functions ◽  
Partial Observation ◽  
Discounted Cost ◽  
Stochastic Filtering ◽  
Observation Process ◽  
The Value Function ◽  
Complete Observation

We consider an infinite horizon optimal control problem for a pure jump Markov process X, taking values in a complete and separable metric space I, with noise-free partial observation. The observation process is defined as Yt = h(Xt), t ≥ 0, where h is a given map defined on I. The observation is noise-free in the sense that the only source of randomness is the process X itself. The aim is to minimize a discounted cost functional. In the first part of the paper we write down an explicit filtering equation and characterize the filtering process as a Piecewise Deterministic Process. In the second part, after transforming the original control problem with partial observation into one with complete observation (the separated problem) using filtering equations, we prove the equivalence of the original and separated problems through an explicit formula linking their respective value functions. The value function of the separated problem is also characterized as the unique fixed point of a suitably defined contraction mapping.

Discrete optimal control with aggregative pole placement

1993 ◽  
Vol 140 (5) ◽  
pp. 309 ◽  
Author(s):  
G. Enea ◽  
J. Duplaix ◽  
M. Franceschi
Keyword(s):  
Optimal Control ◽  
Pole Placement ◽  
Discrete Optimal Control
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