In this paper, we study the optimal control problem of nonlinear differentialinclusions with principle operator being pseudomonotone. First, we give some propertiesof solutions of certain evolution equations. Further,...In this paper, we study the optimal control problem of nonlinear differentialinclusions with principle operator being pseudomonotone. First, we give some propertiesof solutions of certain evolution equations. Further, we prove the existence of admissibletrajectories for evolution inclusions. Then, we extend the Fillipov's selection theoremand discuss a general Lagrange type optimal control problem. Finally, we present anexample that demonstrates the appplicability of our results.展开更多
A method of verifying the viability criterion at a given point for a region with nonsmooth boundary, which is expressed by a quasidifferentiabl function, under a differential inclusion which is a convex hull of finite...A method of verifying the viability criterion at a given point for a region with nonsmooth boundary, which is expressed by a quasidifferentiabl function, under a differential inclusion which is a convex hull of finitely many functions, is proposed. By this method, determining the viability is transformed into solving a number of systems of linear inequalities, or equivalently solving a number of linear programming problems. For the other differential inclusion, called the generalized convex process, it is shown that viability condition holds for a polytope if and only if it holds at all of its vertices. This result is an extension of corresponding one for a linear control system.展开更多
基金Supported by the Natural Science Foundation of Guizhou university(200101007)
文摘In this paper, we study the optimal control problem of nonlinear differentialinclusions with principle operator being pseudomonotone. First, we give some propertiesof solutions of certain evolution equations. Further, we prove the existence of admissibletrajectories for evolution inclusions. Then, we extend the Fillipov's selection theoremand discuss a general Lagrange type optimal control problem. Finally, we present anexample that demonstrates the appplicability of our results.
基金This research is supported by the National Natural Science Foundation of China under Grant No. 10671126 and Shanghai Leading Academic Discipline Project under Grant No. S30501.
文摘A method of verifying the viability criterion at a given point for a region with nonsmooth boundary, which is expressed by a quasidifferentiabl function, under a differential inclusion which is a convex hull of finitely many functions, is proposed. By this method, determining the viability is transformed into solving a number of systems of linear inequalities, or equivalently solving a number of linear programming problems. For the other differential inclusion, called the generalized convex process, it is shown that viability condition holds for a polytope if and only if it holds at all of its vertices. This result is an extension of corresponding one for a linear control system.
