Abstract
In this article, the optimal linear quadratic control problem is considered for the wireless sensor and actuator network with stochastic network-induced delays and packet dropouts. Considering the event-driven relay nodes, the optimal solution is obtained, which is a function of the current plant state and all past control signals. It is shown that the optimal control law is the same for all locations of the controller placement. Since the perfect plant state information is available at the sensor, the optimal controller should be collocated with the sensor. In addition, some issues such as the plant state noise and suboptimal solution are also discussed. The performance of the proposed scheme is investigated by an application of the load frequency control system in power grid.
Highlights
Networked control systems (NCSs) in which the shared communication medium is used for the connection between the plant and the controller have recently attracted much attention due to their potential applications in various areas such as power grids, dc motors, and robotic networks.[1,2] In such systems, the networkinduced delay and the packet dropout introduced by the communication network cause performance degradation and potential system instability.In the literature, network-induced delays have been modeled in various forms such as constant delays,[3] short stochastic delays,[4] and long stochastic delays.[5]
We focus on the general case in which both the stochastic network-induced delays and the packet dropouts are considered, and the optimal control problem is investigated for a linear wireless sensor and actuator networks (WSANs) with event-driven relay nodes
From equations (25) and (26), we observe that the optimal control law Lk is obtained by backward recursion, and the optimal control strategy is linear with the plant state and all past control signals
Summary
Networked control systems (NCSs) in which the shared communication medium is used for the connection between the plant and the controller have recently attracted much attention due to their potential applications in various areas such as power grids, dc motors, and robotic networks.[1,2] In such systems, the networkinduced delay and the packet dropout introduced by the communication network cause performance degradation and potential system instability. We focus on the general case in which both the stochastic network-induced delays and the packet dropouts are considered, and the optimal control problem is investigated for a linear WSAN with event-driven relay nodes. We first assume that the S/A delay is smaller than one sampling period, that is, ttot T , and the results are extended to the large delay case in section ‘‘Extension to the long delay case.’’ Considering the network-induced delay, the dynamic of the controlled plant is given by the following linear continuous-time model where x(t) is an M-dimensional plant state vector, ual ðtÞ is the K-dimensional actuator input, and A and B are known matrices of appropriate sizes. We focus on the optimal control problem of the WSAN with stochastic network-induced delays and packet dropouts. From equations (25) and (26), we observe that the optimal control law Lk is obtained by backward recursion, and the optimal control strategy is linear with the plant state and all past control signals
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