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Gradient flow approach to LQ cost improvement for simultaneous stabilization problem
Author(s) -
Sreeram V.,
Liu W.Q.,
Teo K. L.,
Yan W.Y.
Publication year - 1996
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/(sici)1099-1514(199612)17:5<367::aid-oca579>3.0.co;2-b
Subject(s) - mathematical optimization , control theory (sociology) , balanced flow , quadratic equation , function (biology) , ordinary differential equation , flow (mathematics) , mathematics , optimization problem , matrix (chemical analysis) , transient (computer programming) , differential (mechanical device) , computer science , differential equation , control (management) , engineering , mathematical analysis , materials science , geometry , artificial intelligence , evolutionary biology , composite material , biology , operating system , aerospace engineering
In this paper we consider LQ cost optimization for the simultaneous stabilization problem. The objective is to find a single simultaneously stabilizing feedback gain matrix such that all closed‐loop systems exhibit good transient behaviour. The cost function used is a quadratic function of the system states and the control vector. This paper proposes to seek an optimization solution by solving an ordinary differential equation which is a gradient flow associated with the cost function. Two examples are presented to illustrate the effectiveness of the proposed procedure.