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Serdar Yuksel - One of the best experts on this subject based on the ideXlab platform.

  • weak feller property of non Linear Filters
    Systems & Control Letters, 2019
    Co-Authors: Ali Devran Kara, Naci Saldi, Serdar Yuksel
    Abstract:

    Abstract Weak Feller property of controlled and control-free Markov chains leads to many desirable properties. In control-free setups this leads to the existence of invariant probability measures for compact spaces and applicability of numerical approximation methods. For controlled setups, this leads to existence and approximation results for optimal control policies. We know from stochastic control theory that partially observed systems can be converted to fully observed systems by replacing the original state space with a probability measure-valued state space, with the corresponding kernel acting on probability measures known as the non-Linear Filter process. Establishing sufficient conditions for the weak Feller property for such processes is a significant problem, studied under various assumptions and setups in the literature. In this paper, we prove the weak Feller property of the non-Linear Filter process (i) first under weak continuity of the transition probability of controlled Markov chain and total variation continuity of its observation channel, and then, (ii) under total variation continuity of the transition probability of controlled Markov chain. The former result (i) has first appeared in Feinberg et al. (2016). Here, we present a concise and easy to follow alternative proof for this existing result. The latter result (ii) establishes weak Feller property of non-Linear Filter process under conditions which have not been previously reported in the literature.

  • weak feller property of non Linear Filters
    arXiv: Optimization and Control, 2018
    Co-Authors: Ali Devran Kara, Naci Saldi, Serdar Yuksel
    Abstract:

    Weak Feller property of controlled and control-free Markov chains lead to many desirable properties. In control-free setups this leads to the existence of invariant probability measures for compact spaces and applicability of numerical approximation methods. For controlled setups, this leads to existence and approximation results for optimal control policies. We know from stochastic control theory that partially observed systems can be converted to fully observed systems by replacing the original state space with a probability measure-valued state space, with the corresponding kernel acting on probability measures known as the non-Linear Filter (belief) process. Establishing sufficient conditions for the weak Feller property for such processes is a significant problem, studied under various assumptions and setups in the literature. In this paper, we prove the weak Feller property of the non-Linear Filter process (i) first under weak continuity of the transition probability of controlled Markov chain and total variation continuity of its observation channel, and then, (ii) under total variation continuity of the transition probability of controlled Markov chain. The former result (i) has first appeared in Feinberg et. al. [Math. Oper. Res. 41(2) (2016) 656-681]. Here, we present a concise and easy to follow alternative proof for this existing result. The latter result (ii) establishes weak Feller property of non-Linear Filter process under conditions, which have not been previously reported in the literature.

Ali Devran Kara - One of the best experts on this subject based on the ideXlab platform.

  • weak feller property of non Linear Filters
    Systems & Control Letters, 2019
    Co-Authors: Ali Devran Kara, Naci Saldi, Serdar Yuksel
    Abstract:

    Abstract Weak Feller property of controlled and control-free Markov chains leads to many desirable properties. In control-free setups this leads to the existence of invariant probability measures for compact spaces and applicability of numerical approximation methods. For controlled setups, this leads to existence and approximation results for optimal control policies. We know from stochastic control theory that partially observed systems can be converted to fully observed systems by replacing the original state space with a probability measure-valued state space, with the corresponding kernel acting on probability measures known as the non-Linear Filter process. Establishing sufficient conditions for the weak Feller property for such processes is a significant problem, studied under various assumptions and setups in the literature. In this paper, we prove the weak Feller property of the non-Linear Filter process (i) first under weak continuity of the transition probability of controlled Markov chain and total variation continuity of its observation channel, and then, (ii) under total variation continuity of the transition probability of controlled Markov chain. The former result (i) has first appeared in Feinberg et al. (2016). Here, we present a concise and easy to follow alternative proof for this existing result. The latter result (ii) establishes weak Feller property of non-Linear Filter process under conditions which have not been previously reported in the literature.

  • weak feller property of non Linear Filters
    arXiv: Optimization and Control, 2018
    Co-Authors: Ali Devran Kara, Naci Saldi, Serdar Yuksel
    Abstract:

    Weak Feller property of controlled and control-free Markov chains lead to many desirable properties. In control-free setups this leads to the existence of invariant probability measures for compact spaces and applicability of numerical approximation methods. For controlled setups, this leads to existence and approximation results for optimal control policies. We know from stochastic control theory that partially observed systems can be converted to fully observed systems by replacing the original state space with a probability measure-valued state space, with the corresponding kernel acting on probability measures known as the non-Linear Filter (belief) process. Establishing sufficient conditions for the weak Feller property for such processes is a significant problem, studied under various assumptions and setups in the literature. In this paper, we prove the weak Feller property of the non-Linear Filter process (i) first under weak continuity of the transition probability of controlled Markov chain and total variation continuity of its observation channel, and then, (ii) under total variation continuity of the transition probability of controlled Markov chain. The former result (i) has first appeared in Feinberg et. al. [Math. Oper. Res. 41(2) (2016) 656-681]. Here, we present a concise and easy to follow alternative proof for this existing result. The latter result (ii) establishes weak Feller property of non-Linear Filter process under conditions, which have not been previously reported in the literature.

Richardalain - One of the best experts on this subject based on the ideXlab platform.

Naci Saldi - One of the best experts on this subject based on the ideXlab platform.

  • weak feller property of non Linear Filters
    Systems & Control Letters, 2019
    Co-Authors: Ali Devran Kara, Naci Saldi, Serdar Yuksel
    Abstract:

    Abstract Weak Feller property of controlled and control-free Markov chains leads to many desirable properties. In control-free setups this leads to the existence of invariant probability measures for compact spaces and applicability of numerical approximation methods. For controlled setups, this leads to existence and approximation results for optimal control policies. We know from stochastic control theory that partially observed systems can be converted to fully observed systems by replacing the original state space with a probability measure-valued state space, with the corresponding kernel acting on probability measures known as the non-Linear Filter process. Establishing sufficient conditions for the weak Feller property for such processes is a significant problem, studied under various assumptions and setups in the literature. In this paper, we prove the weak Feller property of the non-Linear Filter process (i) first under weak continuity of the transition probability of controlled Markov chain and total variation continuity of its observation channel, and then, (ii) under total variation continuity of the transition probability of controlled Markov chain. The former result (i) has first appeared in Feinberg et al. (2016). Here, we present a concise and easy to follow alternative proof for this existing result. The latter result (ii) establishes weak Feller property of non-Linear Filter process under conditions which have not been previously reported in the literature.

  • weak feller property of non Linear Filters
    arXiv: Optimization and Control, 2018
    Co-Authors: Ali Devran Kara, Naci Saldi, Serdar Yuksel
    Abstract:

    Weak Feller property of controlled and control-free Markov chains lead to many desirable properties. In control-free setups this leads to the existence of invariant probability measures for compact spaces and applicability of numerical approximation methods. For controlled setups, this leads to existence and approximation results for optimal control policies. We know from stochastic control theory that partially observed systems can be converted to fully observed systems by replacing the original state space with a probability measure-valued state space, with the corresponding kernel acting on probability measures known as the non-Linear Filter (belief) process. Establishing sufficient conditions for the weak Feller property for such processes is a significant problem, studied under various assumptions and setups in the literature. In this paper, we prove the weak Feller property of the non-Linear Filter process (i) first under weak continuity of the transition probability of controlled Markov chain and total variation continuity of its observation channel, and then, (ii) under total variation continuity of the transition probability of controlled Markov chain. The former result (i) has first appeared in Feinberg et. al. [Math. Oper. Res. 41(2) (2016) 656-681]. Here, we present a concise and easy to follow alternative proof for this existing result. The latter result (ii) establishes weak Feller property of non-Linear Filter process under conditions, which have not been previously reported in the literature.

Alain Richard - One of the best experts on this subject based on the ideXlab platform.

  • Regularization aspects in continuous-time model identification
    Automatica, 2005
    Co-Authors: Saïd Moussaoui, David Brie, Alain Richard
    Abstract:

    This paper presents an analysis of some regularization aspects in continuous-time model identification. The study particulary focuses on Linear Filter methods and shows that Filtering the data before estimating their derivatives corresponds to a regularized signal derivative estimation by minimizing a compound criterion whose expression is given explicitly. A new structure based on a null phase Filter corresponding to a true regularization Filter is proposed and allows to discuss the Filter phase effects on parameter estimation by comparing its performances with those of the Poisson Filter-based methods. Based on this analysis, a formulation of continuous-time model identification as a joint system input-output signal and model parameter estimation is suggested. In this framework, two Linear Filter methods are interpreted and a compound criterion is proposed in which the regularization is ensured by a model fitting measure, resulting in a new regularization Filter structure for signal estimation.