Filtering method for linear and non-linear stochastic optimal control of partially observable systems

Delavarkhalafi, Ali; Poursherafatan, Ali

doi:10.2298/fil1719979d

Cited by 3 publications

(6 citation statements)

References 22 publications

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“…It should be mentioned that

Λ_{k, l} = Λ_{l, k}^{*}

and, if M ∈ L ( R n , R n ), the following relation is obtained:

E {(x_{k} - {\overset{x}{true}}_{k})}^{*} M ((), x_{l} - {\overset{true‾}{x}}_{l}) = italictr Λ_{l, k} M .

…”

Section: Spectral Linear Filtermentioning

confidence: 99%

“…It should be mentioned that Λ k,l = Λ * l,k and, if M ∈ L(R n , R n ), the following relation is obtained 10 :…”

Section: Spectral Linear Filtermentioning

confidence: 99%

“…At first, the solution of backward Riccati equation (9) should be found. This solution should be replaced in (10). After that, the solution of (10) can be achieved and the feedback control is obtained as follows 19 :…”

Section: Stochastic Optimal Control Of a Partial Observation Systemmentioning

confidence: 99%

“…In the work of Hafayed et al, the partial information optimal control of mean‐field forward‐backward stochastic system is studied witch driven by orthogonal Teugels martingales, associated with some Lévy processes and an independent Brownian motion. In our previous work, we used filtering method to achieve the optimal control problem of the partially observable system. In this case, the optimal control function is in the drift coefficient of the state process.…”

Section: Introductionmentioning

confidence: 99%

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The spectral linear filter method for a stochastic optimal control problem of partially observable systems

Poursherafatan

Delavarkhalafi

2019

Optim Control Appl Methods

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Summary In this paper, two spectral methods are presented to solve a stochastic optimal control problem of a partially observable system. These two methods work together to solve such problems. In fact, solving such problems involves two cases: obtaining the control function and simulating the partially observable system. At first, a spectral linear filter is defined as a function of time to obtain an appropriate solution for a partially observable system. This linear filter is equipped with an orthogonal basis and it is made to predict the future behavior of this system. In this method, the goal is to approximate the trend of the partially observable system. The second method is suggested to achieve the optimal control corresponding to each sample path. In this method, the spectral Fourier transform is used. These two methods are used together to solve linear and nonlinear cases. In fact, the innovative contents of this paper are both the spectral linear filter and the suggested spectral optimal control method.

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“…It should be mentioned that

Λ_{k, l} = Λ_{l, k}^{*}

and, if M ∈ L ( R n , R n ), the following relation is obtained:

E {(x_{k} - {\overset{x}{true}}_{k})}^{*} M ((), x_{l} - {\overset{true‾}{x}}_{l}) = italictr Λ_{l, k} M .

…”

Section: Spectral Linear Filtermentioning

confidence: 99%

“…It should be mentioned that Λ k,l = Λ * l,k and, if M ∈ L(R n , R n ), the following relation is obtained 10 :…”

Section: Spectral Linear Filtermentioning

confidence: 99%

Section: Stochastic Optimal Control Of a Partial Observation Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The spectral linear filter method for a stochastic optimal control problem of partially observable systems

Poursherafatan

Delavarkhalafi

2019

Optim Control Appl Methods

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“…In this paper we study linear and nonlinear cases of a SOCPP with a control factor on the diffusion part. In fact, it is the second edition of [7] which focuses on SOCPP with a control factor on the diffusion part. We extend the studies of [3,25] to the control diffusion SOCPP and numerical estimation methods.…”

Section: Introductionmentioning

confidence: 99%

Filtering method for linear and non-linear stochastic optimal control of partially observable systems II

Poursherafatan¹,

Delavarkhalafi²

2018

Filomat

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In this paper we studied stochastic optimal control problem based on partially observable systems (SOCPP) with a control factor on the diffusion term. A SOCPP has state and observation processes. This kind of problem has also a minimum payoff function. The payoff function should be minimized according to the partially observable systems consist of the state and observation processes. In this regard, the filtering method is used to evaluat this kind of problem and express full consideration of it. Finally, presented estimation methods are used to simulate the solution of a partially observable system corresponding to the control factor of this problem. These methods are numerically used to solve linear and nonlinear cases.

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On optimal stochastic jumps in multi server queue with impatient customers via stochastic control

Delavarkhalafi

2022

NACO

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<p style='text-indent:20px;'>In this paper, a queuing system as multi server queue, in which customers have a deadline and they request service from a random number of identical severs, is considered. Indeed there are stochastic jumps, in which the time intervals between successive jumps are independent and exponentially distributed. These jumps will be occurred due to a new arrival or situation change of servers. Therefore the queuing system can be controlled by restricting arrivals as well as rate of service for obtaining optimal stochastic jumps. Our model consists of a single queue with infinity capacity and multi server for a Poisson arrival process. This processes contains deterministic rate <inline-formula><tex-math id="M1">\begin{document}$ \lambda(t) $\end{document}</tex-math></inline-formula> and exponential service processes with <inline-formula><tex-math id="M2">\begin{document}$ \mu $\end{document}</tex-math></inline-formula> rate. In this case relevant customers have exponential deadlines until beginning of their service. Our contribution is to extend the Ittimakin and Kao's results to queueing system with impatient customers. We also formulate the aforementioned problem with complete information as a stochastic optimal control. This optimal control law is found through dynamic programming.</p>

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Filtering method for linear and non-linear stochastic optimal control of partially observable systems

Cited by 3 publications

References 22 publications

The spectral linear filter method for a stochastic optimal control problem of partially observable systems

The spectral linear filter method for a stochastic optimal control problem of partially observable systems

Filtering method for linear and non-linear stochastic optimal control of partially observable systems II

On optimal stochastic jumps in multi server queue with impatient customers via stochastic control

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