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NEWTON-METHOD BASED ITERATIVE LEARNING CONTROL METHOD FOR NONLINEAR SYSTEMS T. Lin, D. H. Owens, J. HÃ¤tÃ¶nen Department of Automatic Control and Systems Engineering University of Sheffield, UK
Apply Newton method to the nonlinear equation system
Note that is just the linearisation of the nonlinear system at u k , with z k +1 as the control input and e k as the desired output. Then z k +1 can be acquired by solving the linear ILC problem.
The Newton-method based ILC algorithm is equivalent to the Newton method for nonlinear equations, therefore it should inherit the Newton methodâ€™s convergence properties .
The Newton-Kantrovich Theorem and its proof (Ortega and Rheinboldt, 1970) can be applied to the Newton-method based ILC after slight modification.
Consider the single link direct joint driven manipulator model (Bien and Xu, 1998) on t âˆˆ[0,1]
The reference signal is
T s =0.01 sec is the sampling period.
The initial control input is u 0 =0 . The terminal condition is E =sup [0,1] ( Î¸ d - Î¸ )<1 Ëš. The Norm-Optimal ILC algorithm (Amann et al., 1996) is adopted for solving linear ILC problems.
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