A hybrid observer is described for estimating the state of an $m>0$ channel, $n$-dimensional, continuous-time, linear system of the form $\dot{x}=Ax,y_i=C_{i}x,i\in \{1,2,\dots ,m\}$. The system’s state $x$ is simultaneously estimated by $m$ agents assuming each agent $i$ senses $y_i$ and receives appropriately defined data from each of its current neighbors. Neighbor relations are characterized by a time-varying directed graph $\mathbb{N}\left(t\right)$ whose vertices correspond to agents and whose arcs depict neighbor relations. Agent $i$ updates its estimate $x_i$ of $x$ at “event times” $t_{i1},t_{i2},t_{i3},\dots$ using a local continuous-time linear observer and a local parameter estimator which iterates $q$ times during each event time interval $[t_{i(s-1)},t_{is}),s\ge 1$ to obtain an estimate of $x\left(t_{is}\right)$. Subject to the assumptions that none of the $C_i$’s are zero, the neighbor graph $\mathbb{N}\left(t\right)$ is strongly connected for all time, and the system whose state is to be estimated is jointly observable, it is shown that for any number $\lambda >0$, it is possible to choose $q$ and the local observer gains so that each estimate $x_i$ converges to $x$ at least as fast as $e^{-\lambda t}$ does. This result holds whether or not agents communicate synchronously, although in the asynchronous case it is necessary to assume that $\mathbb{N}\left(t\right)$ changes in a suitably defined sense. Exponential convergence is also assured if the event time sequences of the $m$ agents are slightly different than each other, although in this case only if the system being observed is exponentially stable; this limitation however, is primarily a robustness issue shared by all state estimators, centralized or not, which are operating in “open loop” in the face of small modeling errors. The result also holds facing abrupt changes in the number of vertices and arcs in the inter-agent communication graph upon which the algorithm depends.

描述了一个混合观察者来估计一个状态$米>0$渠道，$n$维，连续时间，形式的线性系统$\dot{X}=\mathrm{一个}X,{\mathrm{是的}}_{\mathrm{一世}}=C_{\mathrm{一世}}X,\mathrm{一世}\in \{1,2,\dots ,米\}$. 系统状态$X$同时估计为$米$代理假设每个代理$\mathrm{一世}$感官${\mathrm{是的}}_{\mathrm{一世}}$并从其当前的每个邻居接收适当定义的数据。邻居关系的特征是时变有向图$\mathbb{ñ}\left(吨\right)$其顶点对应于代理，其弧描述了邻居关系。代理人$\mathrm{一世}$更新其估计$X_{\mathrm{一世}}$的$X$在“活动时间”${吨}_{\mathrm{一世}1},{吨}_{\mathrm{一世}2},{吨}_{\mathrm{一世}3},\dots$使用局部连续时间线性观察器和迭代的局部参数估计器$q$每个事件时间间隔内的次数$[{吨}_{\mathrm{一世}(s-1)},{吨}_{\mathrm{一世}s}),s\ge 1$获得估计$X\left({吨}_{\mathrm{一世}s}\right)$. 前提是假设没有$C_{\mathrm{一世}}$的为零，邻居图$\mathbb{ñ}\left(吨\right)$一直是强连接的，并且要估计其状态的系统是联合可观察的，表明对于任何数$\lambda >0$, 可以选择$q$并且本地观察者的收益使得每个估计$X_{\mathrm{一世}}$收敛到$X$至少和$e^{-\lambda 吨}$做。无论代理是否同步通信，这个结果都成立，尽管在异步情况下有必要假设$\mathbb{ñ}\left(吨\right)$在适当定义的意义上发生变化。如果事件的时间序列也保证指数收敛$米$代理之间略有不同，尽管在这种情况下，仅当被观察的系统呈指数稳定时；然而，这种限制主要是所有状态估计器共享的稳健性问题，无论是否集中，面对小的建模错误，它们在“开环”中运行。该结果还适用于算法所依赖的代理间通信图中顶点和弧的数量的突然变化。