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Polynomial System States (polynomial + system_states)

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Selected Abstracts

Central suboptimal H, filter design for nonlinear polynomial systems

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 10 2009
Michael Basin
Abstract This paper presents the central finite-dimensional H, filter for nonlinear polynomial systems, which is suboptimal for a given threshold , with respect to a modified Bolza,Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the paper reduces the original H, filtering problem to the corresponding optimal H2 filtering problem, using the technique proposed in (IEEE Trans. Automat. Control 1989; 34:831,847). The paper presents the central suboptimal H, filter for the general case of nonlinear polynomial systems based on the optimal H2 filter given in (Int. J. Robust Nonlinear Control 2006; 16:287,298). The central suboptimal H, filter is also derived in a closed finite-dimensional form for third (and less) degree polynomial system states. Numerical simulations are conducted to verify performance of the designed central suboptimal filter for nonlinear polynomial systems against the central suboptimal H, filter available for the corresponding linearized system. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Optimal filtering for incompletely measured polynomial states over linear observations

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 5 2008
Michael Basin
Abstract In this paper, the optimal filtering problem for polynomial system states over linear observations with an arbitrary, not necessarily invertible, observation matrix 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. A transformation of the observation equation is introduced to reduce the original problem to the previously solved one with an invertible observation matrix. The procedure for obtaining a closed system of the filtering equations for any polynomial state 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 a conventional extended Kalman,Bucy filter. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Optimal filtering for polynomial system states with polynomial multiplicative noise

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2006
Michael Basin
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 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. Copyright © 2006 John Wiley & Sons, Ltd. [source]