Linear systems with sparse inputs: Observability and input recovery
Linear systems with sparse inputs: Observability and input recovery
复制标题
具有稀疏输入的线性系统：可观测性和输入恢复
DOI：
10.1109/acc.2015.7172159
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
R. Vidal
中科院分区：
文献类型：
--
作者：
S. Sefati;N. Cowan;R. Vidal
在这项工作中，我们引入了一类新的线性时不变系统，在每个时刻，输入是稀疏的过完备字典的输入。这样的系统可以适合于对表现出由稀疏输入编排的多个离散行为的系统进行建模。虽然假设输入是未知的，我们表明，附加的结构强加于输入允许我们恢复的初始状态和稀疏的，但未知的，仅从输出测量输入。为此，我们推导出充分的可观测性和稀疏恢复条件，将经典的线性系统的可观测性条件与稀疏恢复的不相干条件相结合。我们还提出了一个凸优化算法联合估计的初始条件和恢复稀疏输入。
In this work, we introduce a new class of linear time-invariant systems for which, at each time instant, the input is sparse with respect to an overcomplete dictionary of inputs. Such systems may be appropriate for modeling a system which exhibits multiple discrete behaviors orchestrated by the sparse input. Although the input is assumed to be unknown, we show that the additional structure imposed on the input allows us to recover both the initial state and the sparse, but unknown, input from output measurements alone. For this purpose, we derive sufficient observability and sparse recovery conditions that integrate classical observability conditions for linear systems with incoherence conditions for sparse recovery. We also propose a convex optimization algorithm for jointly estimating the initial condition and recovering the sparse input.