連続系最適制御問題の解の存在定理と数値解の誤差範囲に関する一考察

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  • Exsistance Theorem and Error Bound of Numerical Solutior for Optimal Control Problems of Continuous Systems
  • レンゾクケイ サイテキ セイギョ モンダイ ノ カイ ノ ソンザイ テイリ ト

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Two point boundary value problems formulated from optimal control ploblems of continuous systems contain algebraic equations which give the optimal control. This fact prevents the direct application of the Urabe's theorem by which an approximate solution assures the existence of the theoretical solution and at the same time the error bound of the approximate solution is given. This paper shows the possibility of this application of the theorem using the implicit function theorem. Moreover, even though some tedious calculation is necessary in order to check the conditions of the theorem, this paper shows the methods of conventional calculation at the sacrifice of the mathematical strictness. As an example, using the numerical solution of the optimal control problem of a bilenear system, the exsistence of the theoretical solution is assured and the error bound of the numerical solution is given.

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