MCRF
Cesari-type conditions for semilinear elliptic equation with leading term containing controls
Bo Li Hongwei Lou
An optimal control problem governed by semilinear elliptic partial differential equation is considered. The equation is in divergence form with the leading term containing controls. By studying the $G$-closure of the leading term, an existence result is established under a Cesari-type condition.
keywords: existence condition homogenization Cesari-type condition. elliptic equation Optimal control
MCRF
Optimal blowup/quenching time for controlled autonomous ordinary differential equations
Hongwei Lou Weihan Wang
Blowup/Quenching time optimal control problems for controlled autonomous ordinary differential equations are considered. The main results are maximum principles for these time optimal control problems, including the transversality conditions.
keywords: optimal quenching time Optimal blowup time transversality condition. maximum principle
DCDS-B
Second-order necessary/sufficient conditions for optimal control problems in the absence of linear structure
Hongwei Lou
Second-order necessary conditions for optimal control problems are considered, where the "second-order" is in the sense of that Pontryagin's maximum principle is viewed as a first-order necessary optimality condition. A sufficient condition for a local minimizer is also given.
keywords: ordinary differential equations. optimal control second-order necessary conditions sufficient conditions
MCRF
Second-order necessary conditions for optimal control of semilinear elliptic equations with leading term containing controls
Hongwei Lou Jiongmin Yong

An optimal control problem for a semilinear elliptic equation of divergenceform is considered. Both the leading term and the semilinear term of the state equationcontain the control. The well-known Pontryagin type maximum principle for the optimal controls is the first-order necessary condition. When such a first-order necessary condition is singular in some sense, certain type of the second-order necessary condition will come in naturally. The aim of this paper is to explore such kind of conditions for our optimal control problem.

keywords: Optimal control semilinear elliptic equation control in leading term second-order necessary conditions
MCRF
Time optimal control problems for some non-smooth systems
Hongwei Lou Junjie Wen Yashan Xu
Time optimal control problems for some non-smooth systems in general form are considered. The non-smoothness is caused by singularity. It is proved that Pontryagin's maximum principle holds for at least one optimal relaxed control. Thus, Pontryagin's maximum principle holds when the optimal classical control is a unique optimal relaxed control. By constructing an auxiliary controlled system which admits the original optimal classical control as its unique optimal relaxed control, one get a chance to get Pontryagin's maximum principle for the original optimal classical control. Existence results are also considered.
keywords: optimal quenching time maximum principle monotonicity. existence Optimal blowup time

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