Research And Application Of Finite Time Control Algorithm For Random Jump Positive Syste

The stochastic jump positive systems is a special kind of stochastic systems,and its con-trol strategy and control algorithm design is also the important issues in recent years.Actually,the control analysis and design research for such systems can also be regarded as a problem in the field of computer application technology.At present,most of the research results for stochastic jump positive systems are based on asymptotic stability theory in the infinite in-terval.In fact,it may not be able to meet the actual control requirements if the asymptoti-cally stable systems with poor transient performance,such as severe oscillation or overshoot.Moreover,many actual systems often contain complex characteristics such as mismatched disturbances,nonlinear characteristics,and time-varying parameters,which will also have a certain impact on the system’s stability.Thus,how to design a suitable controller and control algorithm for stochastic jump positive systems is particularly important.Starting from theoretical analysis and application,this thesis studies the controller and control algorithm design problem for stochastic jump positive systems.The main research contents are divided into two parts.The first part studies the finite-time bounded analysis and control algorithm design problem for stochastic Markov jump positive systems with known transition probability information and applied it to jumping neural networks,RL circuit sys-tems,and pest population models.The second part studies the finite-time bounded analysis and control algorithm design problem for stochastic Poisson jump positive systems with un-known transition probability information and applied it to Darboux partial differential equa-tions and network communication systems.The specific research results can be summarized as:·The finite-time boundedness analysis and control algorithm design problems of stochas-tic positive Markov jump neural networks are studied.For the stochastic positive Markov jump neural networks with uncertainties in input-free cases,the finite-time stability issue is analyzed.Then,the finite-time controller and control algorithm is designed to guar-antee the positiveness and finite-time stabilization of the closed-loop stochastic Markov jump neural networks.Finally,the algorithm design steps are given.·The finite-time asynchronous control algorithm design problem of stochastic Markov jump positive systems is studied.Based on the extended state observer（ESO）method,a set of extended variables is introduced to compensate the impact of unmatched dis-turbances in the controlled outputs.The finite-time control algorithm is designed to guarantee the closed-loop stochastic Markov augmented jump systems be positive and finite-time bounded.An RL circuit system has verified the effectiveness of the designed algorithm.By using T-S fuzzy technology,the finite-time L₂asynchronous controller based on a parallel distributed compensation algorithm is designed and a pest population model is given to verify the effectiveness of the designed algorithm.·The finite-time boundedness analysis and control algorithm design problems of stochas-tic positive Poisson jump systems are studied.Considering that the transition probability information is completely unknown,a new model decoupling technique is introduced to solve the coupling problem between the sub-models of the systems.Then,the finite-time L₂controller is designed to guarantee the closed-loop systems be positive and finite-time bounded.Moreover,the algorithm solution process on the basis of matrix squares and polynomials is given.For the stochastic positive 2-D Poisson jump systems with time-varying parameters,the finite-region L₂asynchronous controller is designed to guarantee the closed-loop systems be positive and finite-region bounded.The Darboux partial dif-ferential equation is given to verify the feasibility of the designed algorithm.·The finite-time control algorithm design problem of stochastic positive dual-switching Poisson jump systems is studied.Considering the stochastic positive dual-switching Poisson jump systems with time-varying delay,the finite-time L₂controller,subopti-mal switching algorithm,and control algorithm are designed to guarantee the closed-loop system be positive and finite-time bounded.The network communication model is given to verify the effectiveness of the designed algorithm.