论文标题
使用状态依赖系数参数化用于离散时间非线性系统的SET-MEMBESHIP滤波器
Set-Membership Filter for Discrete-Time Nonlinear Systems Using State Dependent Coefficient Parameterization
论文作者
论文摘要
在此技术说明中，提出了一种递归设置会员滤波算法，用于离散时间非线性动力学系统，但提出了未知但有界的过程和测量噪声。非线性动力学使用状态依赖系数（SDC）参数化以伪线性形式表示。矩阵泰勒的扩展用于扩展有关状态估计的状态依赖性矩阵。在每个时间步骤中使用非自适应随机搜索算法在线计算矩阵taylor扩展中剩余规范的上限。利用这些上限和不确定性的椭圆形设置描述，得出了一个两步滤波器，该滤波器利用标准Kalman滤波器变体的“校正预测”结构。在每个时间步骤中，通过求解相应的半明确程序（SDP）来构建包含系统真实状态的校正和预测椭圆形。最后，包括一个模拟示例，以说明所提出的方法的有效性。
In this technical note, a recursive set-membership filtering algorithm for discrete-time nonlinear dynamical systems subject to unknown but bounded process and measurement noises is proposed. The nonlinear dynamics is represented in a pseudo-linear form using the state dependent coefficient (SDC) parameterization. Matrix Taylor expansions are utilized to expand the state dependent matrices about the state estimates. Upper bounds on the norms of remainders in the matrix Taylor expansions are calculated on-line using a non-adaptive random search algorithm at each time step. Utilizing these upper bounds and the ellipsoidal set description of the uncertainties, a two-step filter is derived that utilizes the `correction-prediction' structure of the standard Kalman Filter variants. At each time step, correction and prediction ellipsoids are constructed that contain the true state of the system by solving the corresponding semi-definite programs (SDPs). Finally, a simulation example is included to illustrate the effectiveness of the proposed approach.
