Open AccessOverview of linear time‐invariant interval observer design: towards a non‐smooth optimisation‐based approach
Author(s) -
Chambon Emmanuel,
Burlion Laurent,
Apkarian Pierre
Publication year - 2016
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2015.0742
Subject(s) - control theory (sociology) , observer (physics) , interval (graph theory) , transformation (genetics) , state vector , lti system theory , computer science , coordinate system , linear system , invariant (physics) , limiting , state (computer science) , mathematics , mathematical optimization , control (management) , algorithm , engineering , artificial intelligence , mathematical analysis , biochemistry , chemistry , physics , classical mechanics , quantum mechanics , combinatorics , mathematical physics , gene , mechanical engineering
Some applications in control require the state vector of a system to be expressed in the appropriate coordinates so as to satisfy to some mathematical properties which constrain the studied system dynamics. This is the case with the theory of linear interval observers which are trivial to implement on cooperative systems, a rather limited class of control systems. The available literature shows how to enforce this limiting cooperativity condition for any considered system through a state‐coordinate transformation. This study proposes an overview of the existing numerical techniques to determine such a transformation. It is shown that in spite of being practical, these techniques have some limitations. Consequently, a reformulation of the problem is proposed so as to apply non‐smooth control design techniques. A solution is obtained in both the continuous‐ and discrete‐time frameworks. Interestingly, the new method allows to formulate additional control constraints. Simulations are performed on three examples.