Lotka-Volterra系统Ⅱ型模糊自适应控制方法

Type-2 fuzzy adaptive control method of Lotka-Volterra system

针对一复杂的Kolmogorov型捕食与被捕食生物系统,基于Ⅱ型模糊集合,提出了一类非线性模糊反馈控制器设计方法,并把逼近误差引入到控制器设计中以改善系统的动态性能;在生物系统受某些外界干扰而使物种无法持续稳定生存的情况下实现对理想状态跟踪,使得跟踪误差收敛到零;并用Lyapunov函数及Ⅱ型模糊逻辑系统的性质证明了所设计的控制器的有效性;从理论上研究了Kolmogorov生态系统的非线性行为及控制,说明该种群最终达到了一个新的适应各物种生存、发展的状态空间.

Considering a class of complicated biomathematic system of preys and predators, a type-2 fuzzy adaptive controller is designed. For bettering the active system properly, the approximated error is introduced into the design of the controller. Finally, the desired state is tracked by system output, until the tracking error is less than a desired threshold when there is outer disturbance. The effectiveness of the controller is proved by Lyapunov function and some properties of type-2 fuzzy logic system. The nonlinear dynamic behavior and control of biomathematic system state are theoretically discussed, which are of practical significance. The scheme indicates that the two creatures would finally reach a good state, which is suitable for them to survive and develop.