当前位置: X-MOL 学术SIAM J. Control Optim. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A Higher-Order Maximum Principle for Impulsive Optimal Control Problems
SIAM Journal on Control and Optimization ( IF 2.2 ) Pub Date : 2020-03-12 , DOI: 10.1137/19m1273785
M. Soledad Aronna , Monica Motta , Franco Rampazzo

SIAM Journal on Control and Optimization, Volume 58, Issue 2, Page 814-844, January 2020.
We consider a nonlinear system, affine with respect to an unbounded control $u$ which is allowed to range in a closed cone. With this system we associate a Bolza type minimum problem, with a Lagrangian having sublinear growth with respect to $u$. This lack of coercivity gives the problem an impulsive character, meaning that minimizing sequences of trajectories happen to converge towards discontinuous paths. As is known, a distributional approach does not make sense in such a nonlinear setting, where, instead, a suitable embedding in the graph space is needed. We provide higher-order necessary optimality conditions for properly defined impulsive minima in the form of equalities and inequalities involving iterated Lie brackets of the dynamical vector fields. These conditions are derived under very weak regularity assumptions and without any constant rank conditions.


中文翻译:

脉冲最优控制问题的高阶最大原理

SIAM控制与优化杂志,第58卷,第2期,第814-844页,2020年1月。
我们考虑一个非线性系统,它相对于无界控制$ u $是仿射的,该无限制控制$ u $可以在一个封闭的圆锥体内变化。通过该系统,我们将Bolza型最小问题与具有相对于$ u $的亚线性增长的Lagrangian关联。矫顽力的缺乏使该问题具有冲动性,这意味着最小化轨迹序列会朝不连续的路径收敛。众所周知,在这种非线性设置中,分配方法没有意义,而是需要在图形空间中进行适当的嵌入。我们为适当定义的脉冲极小值提供了更高阶的必要最优性条件,形式为等式和不等式,涉及动态向量场的迭代李括号。
更新日期:2020-03-12
down
wechat
bug