Direct Collocation with Nonlinear Programming (DCNLP)

による最適制御問題の数値的解法



瀧浦 晃基(東大院), 松尾 弘毅(宇宙研)



最適制御問題における最大の難関である状態量不等式拘束を克服する解法,DCNLPについて述べる.
この方法は,本来時間の連続関数である状態変数と制御入力を離散化し,それらを多項式で補間すること
により最適制御問題を非線形計画法に組み替えて解く解法であり,汎用性と十分な精度を兼ね備えている.
簡単な例題でDCNLPの特性について述べ,より難易度の高い問題については変分法に基づく解法と
比較する.



The numerical solution of the optimal control 

problem by the direct collocation with nonlinear 

programming

Koki TAKIURA

University of Tokyo 

Hiroki MATSUO

Institute of Space and Astronautical Science

We state the direct collocation with nonlinear programming(DCNLP) which can easily solve the 

optimal control problem with state inequality constraints. These constraints are the most difficult points in 

the optimal control problem. In this method we discretize both state and control variables, which are 

originally continuous with respect to time, interpolate them with polynomial functions and convert the 

original optimal control problem into a nonlinear programming(NLP), which is solved numerically. This 

method is applicable to any type of problem and has enough precision. We show numerical examples, 

state the characteristics of DCNLP and compare the result with the solution obtained with the method 

based on calculus of variations.