Control System Design of Nonlinear Systems via Numeric and Symbolic Computation

通过数值和符号计算的非线性系统控制系统设计

• 批准号: 20760280
• 负责人: ICHIHARA Hiroyuki
• 金额: $ 2.5万
• 依托单位: Kyushu Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20760280/
• 关键词: 制御系設計; 数値計算; 数式処理; 二乗和; 限量記号消去法; 限量記号消去; 多項式システム; 制御系解析; 計算機代数; 非線形システム; 線形行列不等式

The research has investigated a methodology of control system design of nonlinear systems, in particular nonlinear polynomial systems via numeric and symbolic computation. The methods of state feedback controller design, observer design and input-to-state system analysis have proposed for nonlinear polynomial systems using sum of squares relaxation and solving semidefinite programming problems. An optimization of nonlinear gain functions has also proposed by a combined use of sum of squares and quantifier elimination. The research also has investigated a design method on gain scheduling controller for the Acrobot, in which effectiveness of several reduction approaches of computation are verified.

研究了非线性系统，特别是非线性多项式系统的控制系统设计方法，通过数值和符号计算。针对非线性多项式系统，提出了利用平方和松弛法和半定规划法设计状态反馈控制器、设计观测器和分析输入-状态系统的方法。本文还提出了一种结合平方和量词消去法的非线性增益函数优化方法。研究了Acrobot增益调度控制器的设计方法，验证了几种降低计算量的方法的有效性。

项目成果

Observer Design for Polynomial Systems with Bounded Disturbances

具有有限扰动的多项式系统的观测器设计

• 发表时间: 2009
• 作者: H.Ichihara;H.Katayama;H.Ichihara;H.Ichihara
• 通讯作者: H.Ichihara

State Feedback Synthesis for Polynomial Systems with Bounded Disturbances, Proc.

具有有限扰动的多项式系统的状态反馈综合，Proc。

• 发表时间: 2008
• 作者: 島津祥徳;波多野雄士;三方康弘;井上晋;H.Ichihara
• 通讯作者: H.Ichihara

Finite time control for linear discrete-time systems

线性离散时间系统的有限时间控制

• 发表时间: 2008
• 作者: 梶洋隆;片山仁志;梶洋隆;片山仁志
• 通讯作者: 片山仁志

Computational Approach to Input-to-State Stability Analysis ofa Class of Nonlinear Systems, Proc.

一类非线性系统输入状态稳定性分析的计算方法，Proc。

• 发表时间: 2009
• 作者: 市原;川田;佐藤昌之;H.Ichihara
• 通讯作者: H.Ichihara

State feedback synthesis for polynomial systems with bounded disturbances

• DOI: 10.1109/cdc.2008.4738610
• 发表时间: 2008-12
• 期刊: 2008 47th IEEE Conference on Decision and Control
• 作者: H. Ichihara