LMI优化算法在陆地自主车控制系统中的应用
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摘要
针对陆地自主车系统以往切换控制在策略选择和系统延时方面的不足,以及在未知情况下外部干扰和测量噪声对控制系统性能的不利影响,提出了一种基于线性矩阵不等式LMI算法的H-infinite非脆弱保性能控制方法。陆地自主车控制系统体现为一类具有范数有界形式参数不确定性的连续广义分段仿射系统,通过采用广义分段仿射Lyapunov函数、投影定理以及几个基本引理,使得由所设计弹性控制器构成的反馈系统既满足鲁棒H-infinite性能指标,又具有二次D-稳定性。使得问题解决转换为一组包含参变量LMIs的求解,进而得到保证此类参数不确定系统具有H-infinite性能的反馈控制器增益矩阵。最终,仿真结果证明了所提方法的有效性,通过比较证实该方法具有一定的理论和实用价值。
In view of the lack of autonomous land vehicle system in previous switching control strategies and system delay,and in the case of unknown external interference and noise on the adverse effects of the performance of the control system,a method of H-infinite non-fragile cost guaranteeing control based on linear matrix inequality LMI algorithm is put forward. Autonomous land vehicle control system is a class of generalized continuous piecewise affine systems with norm bounded parameter uncertainty. Using the generalized Lyapunov function,piecewise affine projection theorem and some basic lemmas,the feedback system composed of the designed elastic controller that not only meets the robust H-infinite performance index,but also has secondary D-stability. By solving a set of LMIs containing parametric variables,a feedback controller gain matrix is obtained to guarantee the H-infinite performance of such continuous descriptor piecewise affine systems. Finally,the effectiveness of the method is proven by the simulation results,and the comparison proves that the proposed method has certain theoretical and practical value.
In view of the lack of autonomous land vehicle system in previous switching control strategies and system delay,and in the case of unknown external interference and noise on the adverse effects of the performance of the control system,a method of H-infinite non-fragile cost guaranteeing control based on linear matrix inequality LMI algorithm is put forward. Autonomous land vehicle control system is a class of generalized continuous piecewise affine systems with norm bounded parameter uncertainty. Using the generalized Lyapunov function,piecewise affine projection theorem and some basic lemmas,the feedback system composed of the designed elastic controller that not only meets the robust H-infinite performance index,but also has secondary D-stability. By solving a set of LMIs containing parametric variables,a feedback controller gain matrix is obtained to guarantee the H-infinite performance of such continuous descriptor piecewise affine systems. Finally,the effectiveness of the method is proven by the simulation results,and the comparison proves that the proposed method has certain theoretical and practical value.
引文
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[3]QIU Jianbin,FENG Gang,GAO Huijun. Approaches to robust static output feedback control of discrete-time piecewise-affine systems with norm-bounded uncertainties[J]. International journal of robust and nonlinear control,2011,21(7):790-814.
[4]RUBAGOTTI M,TRIMBOLI S,BEMPORAD A. Stability and invariance analysis of uncertain discrete-time piecewise affine systems[J]. IEEE transactions on automatic control,2013,58(9):2359-2365.
[5]EGHBAL N,PARIZ N,KARIMPOUR A. Discontinuous piecewise quadratic Lyapunov functions for planar piecewise affine systems[J]. Journal of mathematical analysis and applications,2013,399(2):586-593.
[6]ZHANG Yu,FENG Gang,SUN Jitao. Stability of impulsive piecewise linear systems[J]. International journal of systems science,2013,44(1):139-150.
[7]KAI T,MASUDA R. Limit cycle synthesis of multi-modal and 2-dimensional piecewise affine systems[J]. Mathematical and computer modelling,2012,55(3/4):505-516.
[8]莫以为,萧德云.混合动态系统及其应用综述[J].控制理论与应用,2002,19(1):1-8.
[9]邱剑彬.不确定动态时滞系统的鲁棒滤波设计新方法[D].合肥:中国科学技术大学,2009.
[10]周振华.参数不确定广义分段仿射系统的鲁棒控制和滤波[D].哈尔滨:哈尔滨工业大学,2016.
[11]RODRIGUES L. Dynamic output feedback controller synthesis for piecewise-affine systems[D]. Palo Alto:Stanford University,2002.
[12]刘志林.分段仿射系统的控制器设计及预测控制方法研究[D].哈尔滨:哈尔滨工业大学,2007:106-109.
[13]胡寿松,王执铨,胡维礼.最优控制理论与系统[M].北京:科学出版社,2005.
[14]解学书,钟宜生. H∞控制理论[M].北京:清华大学出版社,1994.
[15]俞立.鲁棒控制:线性矩阵不等式处理方法[M].北京:清华大学出版社,2002.