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Observer‐based controller for constrained uncertain stochastic nonlinear discrete‐time systems
Author(s) -
Hassan Mohamed F.,
Alrifai Muthana T.,
Soliman Hisham M.,
Kourah Mohammed A.
Publication year - 2015
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3396
Subject(s) - control theory (sociology) , extended kalman filter , nonlinear system , robustness (evolution) , observer (physics) , estimator , riccati equation , computer science , algebraic riccati equation , state observer , kalman filter , controller (irrigation) , permanent magnet synchronous generator , mathematics , engineering , control (management) , differential equation , statistics , physics , gene , magnet , mechanical engineering , artificial intelligence , mathematical analysis , chemistry , biology , biochemistry , quantum mechanics , agronomy
Summary In this paper, an observer‐based control approach is proposed for uncertain stochastic nonlinear discrete‐time systems with input constraints. The widely used extended Kalman filter (EKF) is well known to be inadequate for estimating the states of uncertain nonlinear dynamical systems with strong nonlinearities especially if the time horizon of the estimation process is relatively long. Instead, a modified version of the EKF with improved stability and robustness is proposed for estimating the states of such systems. A constrained observer‐based controller is then developed using the state‐dependent Riccati equation approach. Rigorous analysis of the stability of the developed stochastically controlled system is presented. The developed approach is applied to control the performance of a synchronous generator connected to an infinite bus and chaos in permanent magnet synchronous motor. Simulation results of the synchronous generator show that the estimated states resulting from the proposed estimator are stable, whereas those resulting from the EKF diverge. Moreover, satisfactory performance is achieved by applying the developed observer‐based control strategy on the two practical problems. Copyright © 2015 John Wiley & Sons, Ltd.