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ABSTRACT: This paper designs the central finite-dimensional H<sub>∞</sub> filter for linear stochastic systems with integral-quadratically bounded deterministic disturbances, that is sub-optimal for a given threshold y with respect to a modified Bolza-Meyer quadratic criterion including the attenuation control term with the opposite sign. The original H<sub>∞</sub> filtering problem for a linear stochastic system is reduced to the corresponding mean-square H<sub>2</sub> filtering problem, using the technique proposed in [1]. In the example, the designed filter is applied to estimation of the pitch and yaw angles of a two degrees of freedom (2DOF) helicopter.
American Control Conference (ACC), 2011; 08/2011
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ABSTRACT: This paper presents the mean-square filtering problem for incompletely measured polynomial system states, confused with white Poisson noises, over linear observations. The problem is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for any polynomial system state with white Poisson noises over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular case of a third-order state equation. In the example, performance of the designed optimal filter is verified against the conventional mean-square polynomial filter designed for systems with white Gaussian noises.
American Control Conference (ACC), 2011; 08/2011
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ABSTRACT: This paper addresses the mean-square filtering problem for a linear system with Gaussian white noises. The obtained solution contains a sliding mode term, signum of the innovations process. It is shown that the designed sliding mode filter generates the mean-square estimate, which has the same minimum estimation error variance as the best estimate given by the classical Kalman-Bucy filter, although the gain matrices of both filters are different. The theoretical result is complemented with an illustrative example verifying performance of the designed filter. It is demonstrated that the estimates produced by the designed filter and the Kalman-Bucy filter yield the same estimation error variance.
Industrial Technology (ICIT), 2010 IEEE International Conference on; 04/2010
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ABSTRACT: This paper addresses the mean-module filtering problem for a linear system with Gaussian white noises. The obtained solution contains a sliding mode term, signum of the innovations process. It is shown that the designed sliding mode filter generates the mean-module estimate, which yields a better value of the mean-module criterion in comparison to the mean-square Kalman-Bucy filter. To the best of our knowledge, this is the first designed sliding mode filter that is optimal with respect to the mean-module criterion. The theoretical result is complemented with an illustrative example verifying performance of the designed filter, which is compared to the conventional Kalman-Bucy filter. The simulation results confirm an advantage in favor of the designed sliding mode filter.
Industrial Technology (ICIT), 2010 IEEE International Conference on; 04/2010
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ABSTRACT: The risk-sensitive filter design problem with respect to the exponential mean-square criterion is considered for stochastic Gaussian systems with polynomial drift terms and intensity parameters multiplying diffusion terms in the state and observations equations. The closed-form suboptimal filtering algorithm is obtained by linearizing a nonlinear third degree polynomial system at the operating point and reducing the original problem to the optimal filter design for a first degree polynomial system. The reduced filtering problem is solved using quadratic value functions as solutions to the corresponding Fokker-Planck-Kolmogorov equation. The performance of the obtained risk-sensitive filter for stochastic third degree polynomial systems is verified in a numerical example against the mean-square optimal third degree polynomial filter and extended Kalman-Bucy filter, through comparing the exponential mean-square criteria values. The simulation results reveal strong advantages in favor of the designed risk-sensitive algorithm for large values of the intensity parameters.
Control Applications, (CCA) & Intelligent Control, (ISIC), 2009 IEEE; 08/2009
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ABSTRACT: This paper presents the mean-square joint state and diffusion coefficient (noise intensity) estimator for linear stochastic systems with unknown noise intensity over linear observations, where unknown parameters are considered Wiener processes. The original problem is reduced to the filtering problem for an extended state vector that incorporates parameters as additional states. Since the noise intensities cannot be observable in the original linear system, the new quadratic vector variable formed by the diagonal of the matrix square of the system state is introduced. The obtained mean-square filter for the extended state vector also serves as the optimal identifier for the unknown parameters. Performance of the designed mean-square state filter and parameter identifier is verified in an illustrative example.
Electrical Engineering, Computing Science and Automatic Control,CCE,2009 6th International Conference on; 02/2009
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ABSTRACT: The optimal exponential-quadratic control problem and exponential mean-square filtering problems are considered for stochastic Gaussian systems with polynomial first degree drift terms and intensity parameters multiplying diffusion terms in the state and observations equations. The closed form optimal control and filtering algorithms are obtained using quadratic value functions as solutions to the corresponding Hamilton-Jacobi-Bellman equations. The performance of the obtained risk-sensitive regulator and filter for stochastic first degree polynomial systems is verified in a numerical example against the conventional linear-quadratic regulator and Kalman-Bucy filter, through comparing the exponential-quadratic and exponential mean-square criteria values. The simulation results reveal strong advantages in favor of the designed risk-sensitive algorithms in regard to the final criteria values.
Decision and Control, 2008. CDC 2008. 47th IEEE Conference on; 01/2009
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ABSTRACT: In this paper, the optimal filtering problem for polynomial systems with partially measured linear part and polynomial multiplicative noise over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for any polynomial state with partially measured linear part and polynomial multiplicative noise over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular case of a bilinear system state with bilinear multiplicative noise. In the example, the designed optimal filter is applied to solution of the optimal cubic sensor filtering problem, assuming a Gaussian initial condition for the cubic state. The resulting filter yields a reliable and rapidly converging estimate
Decision and Control, 2006 45th IEEE Conference on; 01/2007
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ABSTRACT: This paper presents the optimal filtering and parameter identification problem for linear stochastic systems with unknown multiplicative and additive parameters over linear observations, where unknown parameters are considered Wiener processes. The original problem is reduced to the filtering problem for an extended state vector that incorporates parameters as additional states. The resulting filtering system is bilinear in state, with unmeasured linear part, and linear in observations. The obtained solution is based on the derived optimal filter for bilinear-linear states with partially measured linear part over linear observations. The optimal filter for the extended state vector also serves as the optimal identifier for the unknown parameters. In the example, performance of the designed optimal state filter and parameter identifier is verified for linear systems with unknown multiplicative parameter over linear observations. Both, stable and unstable, linear systems are examined
American Control Conference, 2006; 07/2006
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ABSTRACT: In this paper, the optimal filtering problem for polynomial system states with polynomial multiplicative noise over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for any polynomial state with polynomial multiplicative noise over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular cases of of a linear state equation with linear multiplicative noise and a bilinear state equation with bilinear multiplicative noise. In the example, performance of the designed optimal filter is verified for a quadratic state with a quadratic multiplicative noise over linear observations against the optimal filter for a quadratic state with a state-independent noise and a conventional extended Kalman-Bucy filter
American Control Conference, 2006; 07/2006
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ABSTRACT: In this paper, the optimal filtering problem for polynomial systems with partially measured linear part over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for any polynomial state with partially measured linear part over linear observations with delay is then established, which yields the explicit closed form of the filtering equations in the particular case of a bilinear system state. In the example, performance of the designed optimal filter is verified for a quadratic-linear state with unmeasured linear part over linear observations against the conventionally designed extended Kalman-Bucy filter.
American Control Conference, 2005. Proceedings of the 2005; 07/2005
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ABSTRACT: This paper provides the solution of optimal filtering problems for
the broad class of continuous linear systems with discrete and
continuous measurements, including cases of time-varying sampling
intervals and time-varying measurement delays in discrete and continuous
measurements. The solution is obtained using the integral model of
linear dynamic systems in the form of Ito-Volterra integrals with
discontinuous measures. The developed approach is applicable to linear
systems with discontinuities in states, parameters, controls, and
measurements
Decision and Control, 2001. Proceedings of the 40th IEEE Conference on; 02/2001
