LMIs in Control/pages/Optimal Output Feedback Hinf LMI

Optimal Output Feedback LMIEdit

Optimal output feedback control is a problem which arises from not knowing all information about the output of the system. It correlates to the state feedback situation where the part of the state is unknown. This issue can arise in decentralized control problems, for example, and requires the use of an "observer-like" solution. One such method is the use of a Kalman Filter, a more classical technique. However, other methods exist that do not implement a Kalman Filter such as the one below which uses an LMI to preform the output feeback. The   control methods form an optimization problem which attempts to minimize the   norm of the system.

The SystemEdit

The system is represented using the 9-matrix notation shown below.

 

where   is the state,   is the regulated output,   is the sensed output,   is the exogenous input, and   is the actuator input, at any  .

The DataEdit

 ,  ,  ,  ,  ,  ,  ,  ,   are known.

The LMI: Optimal Output Feedback Control LMIEdit

The following are equivalent.

1) There exists a   such that  

2) There exists  ,  ,  ,  ,  ,  ,   such that

 
 

Conclusion:Edit

The above LMI determines the the upper bound   on the   norm. In addition to this the controller   can also be recovered.

 
 
 
 

where,

 

for any full-rank   and   such that

 .

ImplementationEdit

This implementation requires Yalmip and Sedumi. https://github.com/eoskowro/LMI/blob/master/OF_Hinf.m

Related LMIsEdit

Optimal Output Feedback H2


External LinksEdit

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