State-space Realization of Linear Time-invariant Systems with Maximum Measure of Quality

In this paper, we give a state-space realization that maximizes the measure of quality (MoQ). MoQ of a system is a performance index that determines how easily the system can be controlled, while the standard notion of reachability/controllability just gives a binary information, e.g. reachable or u...

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Bibliographic Details
Published in2019 12th Asian Control Conference (ASCC) pp. 1376 - 1379
Main Authors Sheriff, Mohammed Rayyan, Nagahara, Masaaki
Format Conference Proceeding
LanguageEnglish
Published JSME 01.06.2019
Subjects
Aerospace electronics
Linear systems
Observability
Optimal control
Optimization
Symmetric matrices
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Summary:In this paper, we give a state-space realization that maximizes the measure of quality (MoQ). MoQ of a system is a performance index that determines how easily the system can be controlled, while the standard notion of reachability/controllability just gives a binary information, e.g. reachable or unreachable. In this paper, we formulate the realization problem as maximization of the MoQ by a coordinate transformation matrix. We show that the optimal coordinate transformation is given in a closed form. The proposed method is effective in particular for preconditioning of an ill-conditioned grammian, the inverse of which is used to solve the reachability problem. We show a numerical example to illustrate this merit of the proposed method.