A Recursive Elimination Method for Finite-Horizon Optimal Control Problems of Discrete-Time Rational Systems

In this technical note, a method of solving finite-horizon optimal control problems involving discrete-time rational systems is proposed. Sequences of algebraic equations for the control input and costate at each time are constructed backward, starting from the terminal condition, by the recursive e...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2014-11, Vol.59 (11), p.3081-3086
Main Author: Ohtsuka, Toshiyuki
Format: Article
Language:English
Subjects:
Algebra
Generators
Linear quadratic
Mathematical analysis
Optimal control
Optimization
Polynomials
Recursive
Riccati equations
State feedback
Terminals
Vectors
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Summary:In this technical note, a method of solving finite-horizon optimal control problems involving discrete-time rational systems is proposed. Sequences of algebraic equations for the control input and costate at each time are constructed backward, starting from the terminal condition, by the recursive elimination of variables in the optimality conditions. This recursive elimination can be viewed as a generalization of the classical backward sweep method to obtain the discrete-time Riccati equation for finite-horizon linear quadratic control. Sufficient conditions are given for the existence and uniqueness of locally optimal state feedback laws in the form of algebraic functions of the state.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2014.2321231