LMIs in Control/Click here to continue/Optimal control systems/Mixed H2-Hinf-Optimal Observer
The goal of mixed -optimal state estimation is to design an observer that minimizes the norm of the closed-loop transfer matrix from to , while ensuring that the norm of the closed-loop transfer matrix from to is below a specified bound.
The System edit
Consider the continuous-time generalized plant with state-space realization
where it is assumed that is detectable.
The Data edit
The matrices needed as input are .
The Optimization Problem edit
The observer gain L is to be designed to minimize the norm of the closed-loop transfer matrix from the exogenous input to the performance output while ensuring the norm of the closed-loop transfer matrix from the exogenous input to the performance output is less than , where
is minimized. The form of the observer would be:
is to be designed, where is the observer gain.
The LMI: Optimal Observer edit
The mixed -optimal observer gain is synthesized by solving for , and that minimize subject to ,
Conclusion: edit
The mixed -optimal observer gain is recovered by , the norm of is less than and the norm of T(s) is less than .
Implementation edit
Link to the MATLAB code designing - Optimal Observer
External Links edit
- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
Related LMIs edit