Separation principle for impulse control with partial information

Mazziotto, G.; Szpirglas, J.

doi:10.1080/17442508308833262

Cited by 7 publications

(17 citation statements)

References 26 publications

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“…We prove that the costs associated with the sequence of impulse control problems converge Downloaded by [National Sun Yat-Sen University] at 18: 46 27 December 2014 towards that of the continuous control problem. Each of these impulse control problems with partial observation can be explicitly solved by using the results of [38] or [39]. Thus, we obtain identical infima of the expected cost over the set V of admissible controls and the set & of separated controls (similar result in weak formulation can be found in [20]).…”

Section: Introductionmentioning

confidence: 83%

“…be the family of filtering processes associated with {R',";E E}. It can be proved as in [38] or [39] that the following relation, involving the filtering process fi, holds on {T, 5 t < T, + , ):…”

Section: Set Fib=tj Xiexrb ~ = B ( U ) @ B ( I E ) @ B T and V Amentioning

confidence: 97%

“…By using the results obtained in [38] and [39] for the impulse control of partially observed systems, we explicitly construct a sequence of controls in separated form. We then prove that the optimal cost for the partially observed continuous problem can be approximated as closely as desired by those of impulse control problems.…”

Section: Approximation O F a Stochastic Continuous Problem By Impulsementioning

confidence: 99%

“…[38] or [39] for the case of partially observed systems). For each E, the optimal control depends causally on the filtering process of the system.…”

mentioning

confidence: 98%

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Stochastic continuous control of partially observed systems via impulse control problems

Cohen¹,

Mazziotto²

1989

Stochastics and Stochastic Reports

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The stochastic control problem of partially observed systems is approximated by a sequence of partially observed impulse control problems with non-zero but vanishing impulse costs. For the latter problems, we give an explicit construction of the so-called &-optimal controls in a separated form.As a consequence of this approach, we prove that the infimum of the expected cost over the set of separated controls-i.e. which depend non anticipatively on the filtering process-is equal to the infimum of the expected cost over the set of admissible controls-i.e. which depend non anticipatively on the observation process.For the classical situation of linear systems, this method yields the existence of an optimal separated control.

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Section: Introductionmentioning

confidence: 83%

Section: Set Fib=tj Xiexrb ~ = B ( U ) @ B ( I E ) @ B T and V Amentioning

confidence: 97%

Section: Approximation O F a Stochastic Continuous Problem By Impulsementioning

confidence: 99%

“…[38] or [39] for the case of partially observed systems). For each E, the optimal control depends causally on the filtering process of the system.…”

mentioning

confidence: 98%

See 2 more Smart Citations

Stochastic continuous control of partially observed systems via impulse control problems

Cohen¹,

Mazziotto²

1989

Stochastics and Stochastic Reports

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show abstract

“…This is possible if we can compactify the locally compact state space in such a way that functions defining the cost functional and observation can be extended to continuous functions on the compactification and the Markov semigroup preserves its Feller property on the space of all continuous functions on the compactification In general, however, such compactification does not exist. Another important feature of the present paper is that here we dispense with the finite life time of the state process, a technical assumption imposed in [18].…”

mentioning

confidence: 99%