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2014•Transactions of the Society of Instrument and Control EngineersOpen access

Algebraic Function Solutions to Infinite-horizon Nonlinear Discrete-time Optimal Control Problems

Yu Kawano, Toshiyuki Ohtsuka

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Abstract

In this paper, we give an algebraic characterization of solutions to infinite-horizon nonlinear discrete-time optimal control problems. We define an algebraic function solution to the equation, which is obtained by solving algebraic equations, and derive a necessary and sufficient condition for the existence of an algebraic function solution in terms of commutative algebra. According to our main theorem, obtaining an algebraic solution reduces to finding a specific polynomial ideal.

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What this paper is about

In this paper, we give an algebraic characterization of solutions to infinite-horizon nonlinear discrete-time optimal control problems. We define an algebraic function solution to the equation, which is obtained by solving algebraic equations, and derive a necessary and sufficient condition for the existence of an algebraic function solution in terms of commutative algebra. According to our main theorem, obtaining an algebraic solution reduces to finding a specific polynomial ideal.

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Available abstract

In this paper, we give an algebraic characterization of solutions to infinite-horizon nonlinear discrete-time optimal control problems. We define an algebraic function solution to the equation, which is obtained by solving algebraic equations, and derive a necessary and sufficient condition for the existence of an algebraic function solution in terms of commutative algebra. According to our main theorem, obtaining an algebraic solution reduces to finding a specific polynomial ideal.

Key concepts: Algebraic function, Algebraic solution, Mathematics, Dimension of an algebraic variety, Algebraic number, Real algebraic geometry, Algebraic equation, Function field of an algebraic variety

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