EXISTENCE FOR CALCULUS OF VARIATIONS AND OPTIMAL CONTROL PROBLEMS ON TIME SCALES

Zaidong Zhan; Wei Wei; Yinfei Li; Honglei Xu

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EXISTENCE FOR CALCULUS OF VARIATIONS AND OPTIMAL CONTROL PROBLEMS ON TIME SCALES

机译：时间标度的变量计算和最优控制问题的存在

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In this paper we prove the existence for optimal control problems with terminal constraints on time scales. A definition of the solution of semi-linear control systems involving Sobolev space W_T~(1,2) is proposed and new existence and uniqueness results of this kind of dynamic systems on time scales are presented under a weaker assumption. According to L_T~2 strong-weak lower semi-continuity of integral functionals, we establish the existence of optimal controls. In particular, the existence for calculus of variations on time scales is derived.

机译：在本文中，我们证明了在时标上具有终端约束的最优控制问题的存在。提出了包含Sobolev空间W_T〜（1,2）的半线性控制系统解的定义，并在一个较弱的假设下给出了这种动态系统在时间尺度上的新存在性和唯一性结果。根据积分函数的L_T〜2强弱下半连续性，我们建立了最优控制的存在性。特别地，推导了时间尺度上的变化演算的存在。

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来源
《International Journal of Innovative Computing Information and Control》 |2012年第5b期|p.3793-3808|共16页
作者
Zaidong Zhan; Wei Wei; Yinfei Li; Honglei Xu;
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作者单位

Department of Mathematics Zhejiang University No. 38, Zheda Road, Hangzhou 310027, P. R. China;

Department of Mathematics Guizhou University Huaxi District, Guiyang 550025, P. R. China;

College of Statistics and Mathematics Zhejiang Gongshang University No. 18, Xuezheng Street, Hangzhou 310018, P. R. China;

Department of Statistics and Mathematics Curtin University Perth, WA, 6845, Australia;

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正文语种 eng
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关键词
time scales; existence and uniqueness of solutions of control systems; cal-culus of variations; optimal control;

机译：时间尺度;控制系统解决方案的存在和唯一性;微积分最佳控制;

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1. The Existence of Optimal Controls for Problems Defined on Time Scales [J] . Carlson Dean A. Journal of Optimization Theory and Applications . 2015,第2期

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2. CONDITIONS FOR THE EXISTENCE OF OPTIMAL CONTROL FOR SOME CLASSES OF DIFFERENTIAL EQUATIONS ON TIME SCALES [J] . O. E. Lavrova Journal of Mathematical Sciences . 2017,第3期

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3. Existence of Solutions for Optimal Control Problems on Time Scales whose States are Absolutely Continuous [J] . I.L.D. SANTOS TEMA (So Carlos) . 2016,第1期

机译：状态是绝对连续的时标上最优控制问题的解的存在性
4. Existence of an optimal feedback control law for time-optimal control of two-input analytic nilpotent systems in dimension three [C] . Guoqing Tang . 1998

机译：三维空间中两输入解析零能系统时间最优控制的最优反馈控制律的存在
5. A SINGULAR STOCHASTIC CONTROL PROBLEM ARISING FROM A DETERMINISTIC PROBLEM WITH NON-LIPSCHITZIAN MINIMIZERS (CALCULUS, VARIATIONS, HAMILTON-JACOBI EQUATIONS, OPTIMAL) [D] . HEINRICHER, ARTHUR CYRIL, JR. 1985

机译：由非Lipschitzian最小化子的确定性问题引起的奇异随机控制问题（计算，变量，Hamilton-Jacobi方程，最优）
6. Systematic variations in the content of the purine nucleotides in the steady-state perfused rat heart. Evidence for the existence of controlled storage and release of adenine nucleotides [O] . David J. Bates, David Perrett, John Mowbray 1978

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7. Necessary optimality conditions for the calculus of variations on time scales [O] . Ferreira, Rui A. C., Torres, Delfim F. M. 2007

机译：随时间变化的微积分的必要最优性条件秤
8. Existence Theories for Lagrange and Pontryagin Problems of the Calculus of Variations and Optimal Control. More Dimensional Extensions in Sobolev Spaces [R] . Cesari, L. 1966

机译：Lagrange和pontryagin变分微积分存在理论及最优控制。 sobolev空间中的更多维度扩展

EXISTENCE FOR CALCULUS OF VARIATIONS AND OPTIMAL CONTROL PROBLEMS ON TIME SCALES

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