In this paper,the authors study an optimal control problem governed by a class of multistateordinary differential equations in the absence of convexity.To overcome the difficulty that thecorresponding approximate opti...In this paper,the authors study an optimal control problem governed by a class of multistateordinary differential equations in the absence of convexity.To overcome the difficulty that thecorresponding approximate optimal control problem may have no solution,relaxed controls are introduced.With the help of relaxation theory,Pontryagin's maximum principle for the optimal pairs ofthe original control problem is obtained.In the end of this paper,the authors discuss the applicationof the maximum principle by an example.展开更多
基金supported by the Doctoral Special Foundation of ZHJNC-ZL0904+1 种基金the National Natural Science Foundation of China under Grants Nos.10871039,10601010,and 10826077Guangdong Provincial Natural Science Foundation under Grant No.07301595
文摘In this paper,the authors study an optimal control problem governed by a class of multistateordinary differential equations in the absence of convexity.To overcome the difficulty that thecorresponding approximate optimal control problem may have no solution,relaxed controls are introduced.With the help of relaxation theory,Pontryagin's maximum principle for the optimal pairs ofthe original control problem is obtained.In the end of this paper,the authors discuss the applicationof the maximum principle by an example.
