论文标题
具有不确定输入的连续时间动态系统的状态估计，具有有界变化的输入：熵，比特率和与开关系统的关系
State Estimation of Continuous-time Dynamical Systems with Uncertain Inputs with Bounded Variation: Entropy, Bit Rates, and Relation with Switched Systems
论文作者
论文摘要
我们将Liberzon和Mitra [1]提出的自主动力学系统的估计熵概念扩展到具有有界变化的不确定输入的非线性动力学系统。我们称此新概念为系统的{$ε$} - 系统的估计熵，并表明它降低了状态估计所需的比特率。 {$ε$} - 估计熵表示适合{$ε$}足够最小数量的功能数量的指数率 - 近似于系统的任何轨迹。我们表明，使用跨度或分离轨迹将我们的轨迹与两侧绑定在一起的替代性熵定义。另一方面，我们表明其他常用的熵定义，例如[1]中的熵定义，与无穷大。因此，它们可能不适合具有不确定输入的系统。我们在{$ε$} - 估计熵和估算比特率上得出上限，并将其评估为两个示例。我们提出了一种状态估计算法，该算法构建了一个函数，该函数将给定轨迹近似于{$ε$}误差，给定的时间采样和量化状态和输入的测量值。我们研究了{$ε$} - 估计熵与开关非线性系统的先前概念之间的关系，并为后者提供了新的上限，显示了我们在具有不确定输入的系统上的结果。
We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$ε$}-estimation entropy of the system and show that it lower bounds the bit rate needed for state estimation. {$ε$}-estimation entropy represents the exponential rate of the increase of the minimal number of functions that are adequate for {$ε$}- approximating any trajectory of the system. We show that alternative entropy definitions using spanning or separating trajectories bound ours from both sides. On the other hand, we show that other commonly used definitions of entropy, for example the ones in [1], diverge to infinity. Thus, they are potentially not suitable for systems with uncertain inputs. We derive an upper bound on {$ε$}-estimation entropy and estimation bit rates, and evaluate it for two examples. We present a state estimation algorithm that constructs a function that approximates a given trajectory up to an {$ε$} error, given time-sampled and quantized measurements of state and input. We investigate the relation between {$ε$}-estimation entropy and a previous notion for switched nonlinear systems and derive a new upper bound for the latter, showing the generality of our results on systems with uncertain inputs.
