Controller Design for Polynomial Nonlinear Systems with Affine Uncertain Parameters  

作　　者：TONG Chang-Fei ZHANG Hui SUN You-Xian 

机构地区：[1]State Key Laboratory of Industrial Control Technology, Institute of Industrial Process Control, Zhejiang University, Hangzhou 310027, P. R. China

出　　处：《自动化学报》2007年第12期1321-1325,共5页Acta Automatica Sinica

基　　金：Supported by National Natural Science Foundation of China(60674028,60674071);the Key Technologies R & D Program of Zhejiang Province(2006C11066)

摘　　要：借助于多项式分解，为多项式的一个控制计划有仿射的变化时间的不明确的参数的非线性的系统被介绍。多项式分解的想法是与免费变量把多项式的系数变换成一个矩阵，以便有甚至订单的多项式的 nonnegativity 能被线性矩阵不平等(LMI ) 检查解答者或双线性的矩阵不平等(BMI ) 解答者。为多项式的控制合成非线性的系统在这份报纸基于 Lyapunov 稳定性定理。构造 Lyapunov 功能并且发现反馈控制器被计算机编程自动地完成，算法交上这份报纸。为有相对高顺序的控制器的 multidimension 系统，与完整的单项的底构造的控制器将在众多的术语。克服这个问题，有最小的单项的术语的还原剂形式控制器被建议算法导出。然后，与获得限制瞄准最小的费用性能的非最优的控制被推进。控制计划完成由数字例子说明了的有效性能。By means of polynomial decomposition, a control scheme for polynomial nonlinear systems with affine timevarying uncertain parameters is presented. The idea of polynomial decomposition is to convert the coefficients of polynomial into a matrix with free variables, so that the nonnegativity of polynomials with even orders can be checked by linear matrix inequality （LMI） solvers or bilineax matrix inequality （BMI） solvers. Control synthesis for polynomial nonlinear system is based on Lyapunov stability theorem in this paper. Constructing Lyapunov function and finding feedback controller are automatically finished by computer programming with algorithms given in this paper. For multidimension systems with relatively high-order controller, the controller constructed with full monomial base will be in numerous terms. To overcome this problem, the reduced-form controller with minimum monomial terms is derived by the proposed algorithm. Then a suboptimal control aiming at minimum cost performance with gain constraints is advanced. The control scheme achieves effective performance as illustrated by numerical examples.

关 键 词：控制器 设计 非线性系统 仿射不确定参数 鲁棒控制 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]