On the proof of the existence and uniqueness of minimum-energy control for linear time-invariant systems

Ney Bruno; Jorge Silva Garcia; Paulo Cesar Pellanda

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On the proof of the existence and uniqueness of minimum-energy control for linear time-invariant systems

机译：关于线性时不变系统最小能量控制的存在性和唯一性的证明

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摘要

This paper presents a simple method for determining a minimum-energy input function that takes a controllable linear time-invariant system to any desired state. The method is based upon the idea of formulating the problem as a variational problem under constraint of integral type. The solution is constructive and highly suited to presentation in undergraduate classes in linear systems and control theory, offering a good pedagogical approach for this topic.

机译：本文提出了一种确定最小能量输入函数的简单方法，该函数将可控线性时不变系统带到任何所需状态。该方法基于将问题表述为整数类型约束下的变分问题的思想。该解决方案具有建设性，非常适合在线性系统和控制理论的本科课程中进行介绍，为该主题提供了良好的教学方法。

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来源
《International Journal of Electrical Engineering Education》 |2009年第2期|175-182|共8页
作者
Ney Bruno; Jorge Silva Garcia; Paulo Cesar Pellanda;
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作者单位

Electrical Engineering Department, Military Institute of Engineering, Rio de Janeiro, Brazil;

Electrical Engineering Department, Military Institute of Engineering, Rio de Janeiro, Brazil;

Electrical Engineering Department, Military Institute of Engineering, Rio de Janeiro, Brazil;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
control engineering education; controllability; linear system theory; minimum-energy functions; variational calculus;

机译：控制工程教育;可控性线性系统理论最小能量函数变分演算;

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1. On the proof of the existence and uniqueness of minimum-energy control for linear time-invariant systems [J] . Ney Bruno Jorge Silva Garcia Paulo César Pellanda International Journal of Electrical Engineering Education . 2009,第2期

机译：关于线性时不变系统最小能量控制的存在性和唯一性的证明
2. A concise proof for existence and uniqueness of solutions of linear parabolic PDEs in the context of optimal control [J] . Schiela A. Systems and Control Letters . 2013,第10期

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3. Existence and Uniqueness of Optimal Control of Parabolic Nonlinear Boundary Control System [J] . Kim Sun Ho, Ri Hui Gyong Bulletin of Academy of Sciences of the DPR Korea . 1997,第6期

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4. Optimal control of piecewise deterministic nonlinear systems with controlled transitions: viscosity solutions, their existence and uniqueness [C] . Xiao, M.Q., Basar, . 1999

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6. Existence of unique common solution to the system of non-linear integral equations via fixed point results in incomplete metric spaces [O] . Mian Bahadur Zada, Muhammad Sarwar, Stojan Radenović -1

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7. Linear-quadratic control with and without stability subject to general implicit continuous-time systems: coordinate-free interpretations of the optimal costs in terms of dissipation inequality and linear matrix inequality; existence and uniqueness of optimal controls and state trajectories [O] . Geerts Ton 1994

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8. A Proof of Existence of a Unique Solution to the Problem of Adaptive Beamforming Subject to Linear Constraints [R] . Woollett, M. F. C. 1980

机译：线性约束下自适应波束形成问题唯一解的存在性证明

On the proof of the existence and uniqueness of minimum-energy control for linear time-invariant systems

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