Optimization of second order spatially distributed systems with multiple interconnected actuator/sensor pairs

Iterative learning control for hyperbolic distributed parameter systems based on sensor–actuator networks

“…Remark The system () is a kind of hyperbolic distributed parameter system with Kelvin–Voigt damping and viscous damping based on sensor–actuator networks, which has been frequently applied to describe many physical problems, such as the problem of the movement of chemicals underground and the problem of the transverse displacement of the cable equation with air and structural damping. More details are shown in Demetriou et al [19], Karafyllis et al [20], Feng et al [21], and Karafyllis et al [22]. …”

“…In order to illustrate the effectiveness of the proposed ILC schemes for the hyperbolic DPS () in this paper, the following cable equation which has been studied in Demetriou and Fahroo [19] with air and structural damping considered. $$$$ \left\{\begin{array}{cc}\hfill \frac{\partial^2{x}_k\left(z,t\right)}{\partial {t}^2}& ={\varphi}_1\frac{\partial^2{x}_k\left(z,t\right)}{\partial {z}^2}+{\varphi}_2\frac{\partial^3{x}_k\left(z,t\right)}{\partial t\partial {z}^2}+{\varphi}_3\frac{\partial {x}_k\left(z,t\right)}{\partial t}\hfill \\ {}\hfill & \kern10pt +b\left(z;{z}^a\right){u}_k(t),\hfill \\ {}\hfill {y}_k(t)& ={\int}_0^H\frac{\partial {x}_k\left(z,t\right)}{\partial t}\mathrm{d}z,\hfill \end{array}\right.$$…”

“…𝜕 xk (z,t) 𝜕t in two sides of (19), then integrating with respect to z from 0 to H, it satisfies that…”

“…The proposed hyperbolic distributed parameter systems with sensor–actuator networks are governed by partial differential equations with hyperbolic type, which are a kind of wave equations with Kelvin–Voigt damping and viscous damping. These kind systems have been frequently applied to describe many physical problems, such as the problem of the movement of chemicals underground and the problem of the transverse displacement of the cable equation with air and structural damping, and have been widely studied by Demetriou et al [19], Karafyllis et al [20], Feng et al [21], and Karafyllis et al [22]. Therefore, it makes sense to consider these kind hyperbolic DPSs by using the ILC method.…”

Iterative learning control for semi‐linear distributed parameter systems based on sensor–actuator networks

“…In SANs, the sensors gather information about the physical world and the actuators perform diverse work. Demetriou and Fahroo [6] considered the optimisation problem of second‐order DPSs based on multiple interconnected actuators and sensors pairs. Cai et al .…”