Chapter 5
Higher Order Moment Robust Filtering
for Multi-model Jumping System
This chapter focuses on the high-order moment H ∞ filter design for multi-model
jumping system.
Although certain progress has been obtained in the filtering of multi-model jumping system, these studies are mainly based on the assumption that the state and the
unknown disturbances of the systems are subject to a Gaussian distribution. In this
case, it is enough to estimate the system dynamics based only on the mean or mean
square error.
However, in most scenarios, system dynamics cannot be described by Gaussian
distributions and it is difficult to estimate the state accurately based only on the mean
and mean square error. For example, unavoidable errors will result if high-order
moment information is not incorporated such as the skewness in economy systems
[253]. Therefore, it is necessary to take the high-order moment characteristics into
consideration during the filter design. In [37], the cumulant generating function
(CGF) was used to analyze the higher-order moment stability of multi-model jumping
system and this method provides a new approach to estimate the system state based
on high-order moment characteristics. However, the authors in [37] only investigated
stability conditions for the multi-model jumping system; high-order moment issues
still warrant greater exploration, particularly control synthesis problems and filtering
issues. Issues related to high-order moment filtering will be thus investigated in this
chapter.
Firstly, the high-order moment H ∞ filtering issues for multi-model jumping system is addressed. A deterministic high-order component expression of original multimodel jumping system is obtained via the cumulant generating function. In split
of the obtained high-order component expression, the high-order moment filter of
multi-model jumping system is designed.
Then, considering the finite frequency characteristics of unknown disturbances,
a new approach is provided based on GKYP lemma. In this case, it addresses simultaneously determination of high-order moment and finite frequency filtering issues.
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
S. He and X. Luan, Multi-model Jumping Systems: Robust Filtering and Fault Detection,
https://doi.org/10.1007/978-981-33-6474-5_5
73
Higher Order Moment Robust Filtering
for Multi-model Jumping System
This chapter focuses on the high-order moment H ∞ filter design for multi-model
jumping system.
Although certain progress has been obtained in the filtering of multi-model jumping system, these studies are mainly based on the assumption that the state and the
unknown disturbances of the systems are subject to a Gaussian distribution. In this
case, it is enough to estimate the system dynamics based only on the mean or mean
square error.
However, in most scenarios, system dynamics cannot be described by Gaussian
distributions and it is difficult to estimate the state accurately based only on the mean
and mean square error. For example, unavoidable errors will result if high-order
moment information is not incorporated such as the skewness in economy systems
[253]. Therefore, it is necessary to take the high-order moment characteristics into
consideration during the filter design. In [37], the cumulant generating function
(CGF) was used to analyze the higher-order moment stability of multi-model jumping
system and this method provides a new approach to estimate the system state based
on high-order moment characteristics. However, the authors in [37] only investigated
stability conditions for the multi-model jumping system; high-order moment issues
still warrant greater exploration, particularly control synthesis problems and filtering
issues. Issues related to high-order moment filtering will be thus investigated in this
chapter.
Firstly, the high-order moment H ∞ filtering issues for multi-model jumping system is addressed. A deterministic high-order component expression of original multimodel jumping system is obtained via the cumulant generating function. In split
of the obtained high-order component expression, the high-order moment filter of
multi-model jumping system is designed.
Then, considering the finite frequency characteristics of unknown disturbances,
a new approach is provided based on GKYP lemma. In this case, it addresses simultaneously determination of high-order moment and finite frequency filtering issues.
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
S. He and X. Luan, Multi-model Jumping Systems: Robust Filtering and Fault Detection,
https://doi.org/10.1007/978-981-33-6474-5_5
73