Discrete-Time Nonlinear Optimal Control via Generating Functions

Dijian CHEN
Tatsuya SUZUKI

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E99-A    No.11    pp.2037-2048
Publication Date: 2016/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E99.A.2037
Type of Manuscript: PAPER
Category: Systems and Control
generating function,  nonlinear,  optimal control,  tensor notation,  

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This paper develops the generating function method for the discrete-time nonlinear optimal control problem. This method can analytically give the optimal input as state feedforward control in terms of the generating functions. Since the generating functions are nonlinear, we also develop numerical implementations to find their Taylor series expressions. This finally gives optimal solutions expressed only in terms of the pre-computed generating function coefficients and state boundary conditions, such that it is useful for the on-demand optimal solution generation for different boundary conditions. Examples demonstrate the effectiveness of the developed method.