A novel Krein space approach to robust H∞ filtering for linear uncertain systems is developed. The parameter uncertainty, entering into both states and measurement equations, satisfies an energy-type constraint. Then...A novel Krein space approach to robust H∞ filtering for linear uncertain systems is developed. The parameter uncertainty, entering into both states and measurement equations, satisfies an energy-type constraint. Then a Krein space approach is used to tackle the robust H∞ filtering problem. To this end, a new Krein space formal system is designed according to the original sum quadratic constraint （SQC） without introducing any nonzero factors into it and, consequently, the estimate recursion is obtained through the filter gain in Krein space. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.展开更多
针对一类具有多项式向量场的仿射型不确定非线性系统,给出一种基于多项式平方和(sum of squares,SOS)技术的鲁棒H∞状态反馈控制器设计方法.该方法的优点在于控制器的设计避开了直接求解复杂的哈密尔顿-雅可比不等式(Hamilton Jacobi in...针对一类具有多项式向量场的仿射型不确定非线性系统,给出一种基于多项式平方和(sum of squares,SOS)技术的鲁棒H∞状态反馈控制器设计方法.该方法的优点在于控制器的设计避开了直接求解复杂的哈密尔顿-雅可比不等式(Hamilton Jacobi inequality,HJI)和构造Lyapunov函数带来的困难.将鲁棒稳定性分析和控制器设计问题转化为求解以Lyapunov函数为参数的矩阵不等式,该类不等式可利用SOS技术直接求解.此外,在前文基础上研究了基于SOS规划理论与S-procedure技术的局部稳定鲁棒H∞控制器设计方法.最后以非线性质量弹簧阻尼系统作为仿真算例验证该方法的有效性.展开更多
为缓解移动机器人同步定位与构图(Simultaneous Localization and Mapping,SLAM)在恶劣噪声干扰下存在估计精度低、不一致及鲁棒性差的问题,提出一种新颖的基于迭代无迹H_∞滤波的SLAM算法。所提算法将无迹变换融入到扩展H_∞滤波中,以...为缓解移动机器人同步定位与构图(Simultaneous Localization and Mapping,SLAM)在恶劣噪声干扰下存在估计精度低、不一致及鲁棒性差的问题,提出一种新颖的基于迭代无迹H_∞滤波的SLAM算法。所提算法将无迹变换融入到扩展H_∞滤波中,以此估计系统状态均值和协方差,无需推导Jacobian矩阵,避免了线性化误差积累,增强了算法的数值稳定性;此外,通过迭代更新方式,利用观测信息不断校正系统状态均值和协方差,进一步减小估计误差。在仿真实验中,在不同环境和不同噪声下对比分析所提算法、EKF-SLAM、UKF-SLAM及CEHF-SLAM。结果表明所提算法在不同恶劣噪声干扰下依然能保持高的估计精度和强鲁棒性,并能适应不同的环境,是一种有效且可行的SLAM算法。展开更多
基金Supported by National Natural Science Foundation of China （10571036） the Key Discipline Development Program of Beijing Municipal Commission （XK100080537）
基金supported by the National Natural Science Foundation of China (51179039)the Ph.D. Programs Foundation of Ministry of Education of China (20102304110021)
文摘A novel Krein space approach to robust H∞ filtering for linear uncertain systems is developed. The parameter uncertainty, entering into both states and measurement equations, satisfies an energy-type constraint. Then a Krein space approach is used to tackle the robust H∞ filtering problem. To this end, a new Krein space formal system is designed according to the original sum quadratic constraint （SQC） without introducing any nonzero factors into it and, consequently, the estimate recursion is obtained through the filter gain in Krein space. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.
文摘针对一类具有多项式向量场的仿射型不确定非线性系统,给出一种基于多项式平方和(sum of squares,SOS)技术的鲁棒H∞状态反馈控制器设计方法.该方法的优点在于控制器的设计避开了直接求解复杂的哈密尔顿-雅可比不等式(Hamilton Jacobi inequality,HJI)和构造Lyapunov函数带来的困难.将鲁棒稳定性分析和控制器设计问题转化为求解以Lyapunov函数为参数的矩阵不等式,该类不等式可利用SOS技术直接求解.此外,在前文基础上研究了基于SOS规划理论与S-procedure技术的局部稳定鲁棒H∞控制器设计方法.最后以非线性质量弹簧阻尼系统作为仿真算例验证该方法的有效性.
文摘为缓解移动机器人同步定位与构图(Simultaneous Localization and Mapping,SLAM)在恶劣噪声干扰下存在估计精度低、不一致及鲁棒性差的问题,提出一种新颖的基于迭代无迹H_∞滤波的SLAM算法。所提算法将无迹变换融入到扩展H_∞滤波中,以此估计系统状态均值和协方差,无需推导Jacobian矩阵,避免了线性化误差积累,增强了算法的数值稳定性;此外,通过迭代更新方式,利用观测信息不断校正系统状态均值和协方差,进一步减小估计误差。在仿真实验中,在不同环境和不同噪声下对比分析所提算法、EKF-SLAM、UKF-SLAM及CEHF-SLAM。结果表明所提算法在不同恶劣噪声干扰下依然能保持高的估计精度和强鲁棒性,并能适应不同的环境,是一种有效且可行的SLAM算法。
