Hilbert空間における双対準Newton法とその状態制約最適制御問題への応用

概要

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Quasi-Newton methods are extended to optimization problems with an operator constraint in Hilbert spaces. In these algorithms, quadratic programming subproblems with a set constraint are iteratively solved to obtain estimates of Lagrange multipliers, and a sequence of search directions is generated with these estimates.Then these methods are applied to optimal control problems with state inequality constraints. In this case, the control problem is reduced to a series of nonnegatively constrained quadratic programming problems in a function space and they can be easily solved, e.g., by clipping-off techniques. A numerical example is also presented to illustrate the usefulness of the proposed algorithm.
公益社団法人計測自動制御学会の論文