Polynomial filtering for nonlinear stochastic systems with state‐ and disturbance‐dependent noises

Abstract

This article is concerned with the polynomial filtering problem for a class of nonlinear stochastic systems governed by the Itô differential equation. The system under investigation involves polynomial nonlinearities, unknown-but-bounded disturbances, and state-and disturbance-dependent noises ((x, d)-dependent noises for short). By expanding the polynomial nonlinear functions in Taylor series around the state estimate, a new polynomial filter design method is developed with hope to reduce the conservatism of the existing results. In virtue of stochastic analysis and inequality technique, sufficient conditions in terms of parameter-dependent linear matrix inequalities (PDLMIs) are derived to guarantee that the estimation error system is input-to-state stable in probability. Moreover, the desired polynomial matrix can be obtained by solving the PDLMIs via the sum-of-squares approach. The effectiveness and applicability of the proposed method are illustrated by two numerical examples with one concerning the permanent magnet synchronous motor.

Developing an innovative method to control the probability density function shape of the state response for nonlinear stochastic systems

“…In practice, stochasticity is one of the main contributors to system complexities 1 . Most control systems are inevitably disturbed by random noise, so every system in the natural world can be considered a stochastic system.…”

Centralized moving‐horizon estimation for a class of nonlinear dynamical complex networks under event‐triggered transmission scheme

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Consensus‐based unscented Kalman filtering over sensor networks with communication protocols

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