As environmental pollution and safety of human and creatures have been an issue of concern, pest management based on nonchemical use is preferable. Biological pest control can satisfy the regulation of pest population without causing environmental problems. Moreover, representation of dynamical systems in the form of fractional-order dynamic models can explain several phenomena better than the integer-order dynamic models can. The aim of this study is to determine the biological pest control policy for the fractional-order pest control systems, which is a complex nonlinear multiple input and multiple output control problem. Here, the system is represented in the form of a fractional-order Lotka–Volterra model. In order to avoid complexity in the nonlinear feedback controller design process, the tensor product (TP) model transformation was applied to automatically transform the biological pest control system to the TP polytopic model which allows the designer to synthesize the controller under linear framework. Moreover, the design process can be easily carried out by solving an linear matrix inequality (LMI) problem, which is very well applicable to high-dimensional multiple input and multiple output control problems. Simulation studies were conducted to demonstrate the ease of the TP-based design process. The simulation results showed that the designed control policy effectively manipulates the pest populations of the fractional-order Lotka–Volterra model to the desired level which is economically viable.

中文翻译：

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基于张量积模型变换的分数阶生物害虫防治系统控制

由于环境污染和人类和生物的安全一直是一个令人关注的问题，因此基于非化学使用的害虫管理是更可取的。生物害虫防治可以满足对害虫种群的调控，同时不会造成环境问题。此外，以分数阶动态模型形式表示的动态系统可以比整数阶动态模型更好地解释多种现象。本研究的目的是确定分数阶害虫控制系统的生物害虫控制策略，这是一个复杂的非线性多输入多输出控制问题。在这里，系统以分数阶 Lotka-Volterra 模型的形式表示。为了避免非线性反馈控制器设计过程的复杂性，应用张量积（TP）模型转换将生物害虫控制系统自动转换为TP多面体模型，允许设计者在线性框架下合成控制器。此外，设计过程可以通过求解线性矩阵不等式 (LMI) 问题轻松进行，非常适用于高维多输入多输出控制问题。进行了仿真研究以证明基于 TP 的设计过程的简便性。模拟结果表明，设计的控制策略有效地将分数阶 Lotka-Volterra 模型的害虫种群控制到经济上可行的所需水平。