Finite-time stability and optimal control of a stochastic reaction-diffusion model for Alzheimer’s disease with impulse and time-varying delay

2021 ◽  
Author(s):  
Jing Hu ◽  
Qimin Zhang ◽  
Anke Meyer-Baese ◽  
Ming Yea
Keyword(s):  
Optimal Control ◽  
Finite Time ◽  
Reaction Diffusion ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Reaction Diffusion Model ◽  
Stochastic Reaction ◽  
Varying Delay

scholarly journals Finite-time stability and optimal control of an impulsive stochastic reaction-diffusion vegetation-water system driven by L$ {\rm \acute{e}} $vy process with time-varying delay

2021 ◽  
Vol 18 (6) ◽  
pp. 8462-8498
Author(s):  
Zixiao Xiong ◽  
◽  
Xining Li ◽  
Ming Ye ◽  
Qimin Zhang ◽  
...  
Keyword(s):  
Optimal Control ◽  
Finite Time ◽  
Water System ◽  
Reaction Diffusion ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Vegetation Water ◽  
Varying Delay

<abstract><p>In this paper, a reaction-diffusion vegetation-water system with time-varying delay, impulse and L$ {\rm \acute{e}} $vy jump is proposed. The existence and uniqueness of the positive solution are proved. Meanwhile, mainly through the principle of comparison, we obtain the sufficient conditions for finite-time stability which reflect the effect of time delay, diffusion, impulse, and noise. Besides, considering the planting, irrigation and other measures, we introduce control variable into the vegetation-water system. In order to save the costs of strategies, the optimal control is analyzed by using the minimum principle. Finally, numerical simulations are shown to illustrate the effectiveness of our theoretical results.</p></abstract>

scholarly journals NEW RESULTS ON FINITE-TIME STABILITY FOR NONLINEAR FRACTIONAL ORDER LARGE SCALE SYSTEMS WITH TIME VARYING DELAY AND INTERCONNECTIONS

2020 ◽  
Vol 225 (02) ◽  
pp. 52-57
Author(s):  
Phạm Ngọc Anh ◽  
Nguyễn Trường Thanh ◽  
Hoàng Ngọc Tùng
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Large Scale ◽  
Time Varying ◽  
Time Stability ◽  
Large Scale Systems ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Varying Delay

Bài báo này khảo sát tính ổn định hữu hạn của một lớp hệ quy mô lớn cấp phân số có trễ biến thiên và nhiễu phi tuyến. Sử dụng bất đẳng thức Gronwall tổng quát, một điều kiện đủ cho ổn định hữu hạn của các hệ này được thiết lập thông qua hàm Mittag-Leffler. Kết quả thu được sau đó được áp dụng cho hệ bất định và hệ không ôtonom có trễ biến thiên và nhiễu phi tuyến.

scholarly journals Fuzzy Finite-Time Stability of Chaotic Systems with Time-Varying Delay and Parameter Uncertainties

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Dong Li ◽  
Jinde Cao
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Time Varying ◽  
Time Stability ◽  
Parameter Uncertainties ◽  
New Model ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
S Model ◽  
Varying Delay

This paper discusses the finite-time stability of chaotic systems with time-varying delay and parameter uncertainties. A new model based on Takagi-Sugeno (T-S) model is proposed for representing chaotic systems. By the new model, finite-time stability of chaotic systems can be converted into stabilization of fuzzy T-S systems with parameter uncertainties. A sufficient condition is given in terms of matrix inequalities, which guarantees the finite-time stability for fuzzy systems can be achieved. Numerical simulations on the chaotic systems are presented to demonstrate the effectiveness of the theoretical results.

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