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EXTENSION OF KALMAN FILTER THEORY TO NONLINEAR SYSTEMS WITH APPLICATION TO WING ROCK MOTION
Author(s) -
Shue ShyhPyng,
Agarwal Ramesh K.
Publication year - 2000
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1111/j.1934-6093.2000.tb00144.x
Subject(s) - mathematics , control theory (sociology) , lyapunov function , kalman filter , algebraic riccati equation , state vector , nonlinear system , riccati equation , lyapunov equation , mathematical analysis , computer science , differential equation , control (management) , physics , statistics , classical mechanics , quantum mechanics , artificial intelligence
A formulation for nonlinear Kalman filter theory is developed in this paper. It is shown that the solution of the nonlinear Kalman filter problem is governed by a Hamilton‐Jacobi‐Bellman inequality (HJBI). Choosing the closed loop Lyapunov function in a symmetric matrix form of the state vector results in the reduction of the HJBI to an algebraic Riccati inequality along with several other algebraic inequalities. These inequalities are formulated into a series of closed loop Lyapunov inequalities which are turned into equalities by adding a positive state vector function. Closed loop Lyapunov functions are then obtained successively by solving these eqauations based on the powers of the state vector. Control of a nonlinear wing rock motion is employed as an example to illustrate the theory.