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Analysis of Nonlinear Quadratic Control in Infinite Time
Author(s) -
Popescu Mihai
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810899
Subject(s) - mathematics , riccati equation , algebraic riccati equation , quadratic equation , state variable , matrix (chemical analysis) , variable (mathematics) , bilinear interpolation , nonlinear system , state (computer science) , differential equation , control variable , differential (mechanical device) , mathematical analysis , physics , statistics , geometry , materials science , algorithm , quantum mechanics , composite material , thermodynamics
This study refers to minimization of quadratic functionals in infinite time. The coefficients of the quadratic form are quadratic matrices, function of the state variable. Dynamic constraints are represented by a bilinear differential systems of the form. The necessary extremum conditions determine the adjoint variables λ and the control variables u as functions of state variable, respectively the adjoint system corresponding to those functions. Thus it will be obtained a matrix differential equation where the solution representing the positive defined symmetric matrix P ( x ), verifies the Riccati algebraic equation. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)