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→Dissipative systems in control theory
最近的研究重新考虑了Prigogine的耗散结构思想与生物系统的关系。
最近的研究重新考虑了Prigogine的耗散结构思想与生物系统的关系。
== Dissipative systems in control theory ==
== 控制论中的耗散系统 Dissipative systems in control theory ==
In systems theory the concept of dissipativity was first introduced by [[Jan Camiel Willems|Willems]],<ref>{{cite journal |last1=Willems |first1=J.C. |title=Dissipative dynamical systems part 1: General theory |journal=Arch. Rational Mech. Anal. |date=1972 |volume=45 |issue=5 |page=321 |doi=10.1007/BF00276493 |bibcode=1972ArRMA..45..321W |hdl=10338.dmlcz/135639 |url=http://dml.cz/bitstream/handle/10338.dmlcz/135639/Kybernetika_41-2005-1_5.pdf }}</ref> which describes dynamical systems by input-output properties. Considering a dynamical system described by its state <math> x(t) </math>, its input <math>u(t)</math> and its output <math>y(t)</math>, the input-output correlation is given a supply rate <math> w(u(t),y(t))</math>. A system is said to be dissipative with respect to a supply rate if there exists a continuously differentiable storage function <math> V(x(t))</math> such that <math>V(0)=0</math>, <math>V(x(t))\ge 0 </math> and
In systems theory the concept of dissipativity was first introduced by [[Jan Camiel Willems|Willems]],<ref>{{cite journal |last1=Willems |first1=J.C. |title=Dissipative dynamical systems part 1: General theory |journal=Arch. Rational Mech. Anal. |date=1972 |volume=45 |issue=5 |page=321 |doi=10.1007/BF00276493 |bibcode=1972ArRMA..45..321W |hdl=10338.dmlcz/135639 |url=http://dml.cz/bitstream/handle/10338.dmlcz/135639/Kybernetika_41-2005-1_5.pdf }}</ref> which describes dynamical systems by input-output properties. Considering a dynamical system described by its state <math> x(t) </math>, its input <math>u(t)</math> and its output <math>y(t)</math>, the input-output correlation is given a supply rate <math> w(u(t),y(t))</math>. A system is said to be dissipative with respect to a supply rate if there exists a continuously differentiable storage function <math> V(x(t))</math> such that <math>V(0)=0</math>, <math>V(x(t))\ge 0 </math> and
In systems theory the concept of dissipativity was first introduced by Willems, which describes dynamical systems by input-output properties. Considering a dynamical system described by its state <math> x(t) </math>, its input <math>u(t)</math> and its output <math>y(t)</math>, the input-output correlation is given a supply rate <math> w(u(t),y(t))</math>. A system is said to be dissipative with respect to a supply rate if there exists a continuously differentiable storage function <math> V(x(t))</math> such that <math>V(0)=0</math>, <math>V(x(t))\ge 0 </math> and
In systems theory the concept of dissipativity was first introduced by Willems, which describes dynamical systems by input-output properties. Considering a dynamical system described by its state <math> x(t) </math>, its input <math>u(t)</math> and its output <math>y(t)</math>, the input-output correlation is given a supply rate <math> w(u(t),y(t))</math>. A system is said to be dissipative with respect to a supply rate if there exists a continuously differentiable storage function <math> V(x(t))</math> such that <math>V(0)=0</math>, <math>V(x(t))\ge 0 </math> and
在系统论中，耗散性的概念是由 Willems 首先提出的，它通过输入输出的性质来描述动态系统。考虑一个由状态数学 x (t) / math 描述的动力系统，它的输入数学 u (t) / math 和输出数学 y (t) / math，输入输出相关性被给出一个供给率数学 w (u (t) ，y (t) / math。如果存在一个连续可微的存储函数数学 v (x (t)) / 这样的数学 v (0)0 / math，数学 v (x (t)) ge0 / math，那么系统相对于供给率是耗散的
在系统论中，耗散性的概念是由 Jan Camiel Willems 首先提出的，它通过输入输出的性质来描述动态系统。考虑一个由状态 x (t) / math 描述的动力系统，它的输入数学 u (t) / math 和输出数学 y (t) / math，输入输出相关性被给出一个供给率数学 w (u (t) ，y (t) / math。如果存在一个连续可微的存储函数数学 v (x (t)) / 这样的数学 v (0)0 / math，数学 v (x (t)) ge0 / math，那么系统相对于供给率是耗散的
耗散性理论对于线性和非线性系统的反馈控制律设计具有一定的参考价值。耗散系统理论已由 v.m。波波夫，J.C.Willems，d.j。希尔和 p. 莫伊兰。在线性不变系统的情况下，这被称为正实传递函数，一个基本的工具是所谓的 Kalman-Yakubovich-Popov 引理，它把正实系统的状态空间和频域性质联系起来。由于耗散系统的重要应用，它仍然是系统与控制研究的一个活跃领域。
耗散性理论对于线性和非线性系统的反馈控制律设计具有一定的参考价值。耗散系统理论已由 v.m。波波夫，J.C.Willems，d.j。希尔和 p. 莫伊兰。在线性不变系统的情况下，这被称为正实传递函数，一个基本的工具是所谓的 Kalman-Yakubovich-Popov 引理，它把正实系统的状态空间和频域性质联系起来。由于耗散系统的重要应用，它仍然是系统与控制研究的一个活跃领域。
== Quantum dissipative systems ==
== Quantum dissipative systems ==