一类非线性区间时滞随机系统的控制与仿真

Control and Simulation for a Class of Nonlinear Interval Delay Stochastic Systems

针对一类非线性区间时滞随机系统的控制问题,提出一种基于随机模糊双曲正切模型的时滞依赖控制策略。应用随机模糊双曲正切模型对非线性随机系统进行建模,其中模型参数可用BP神经网络进行学习。提出一个新颖的Lyapunov-Krasovskii泛函进而推导出闭环系统时滞依赖均方意义渐近稳定的镇定条件。最后采用改进的Euler-Maruyama法对非线性随机微分方程进行仿真,仿真结果验证了所提出的控制策略的有效性。

The problem of control and simulation for a class of nonlinear stochastic systems with interval delay was investigated, and delay-dependent control law was proposed based on the stochastic fuzzy hyperbolic tangent model （SFHM）. The underlying nonlinear system could be modeled by the SFHM whose model parameters could be learned by BP neural network. The asymptotical stability condition in the mean square sense for the closed systems was derived by applying a new Lyapunov-Krasovskii functional. Finally, an improved Euler-Maruyamma numerical method for nonlinear stochastic differential function was proposed to illustrate the efficiency of the resulted control strategy.