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Rapid exponential stabilization of nonlinear continuous systems via event-triggered impulsive control

Dlala Mohsen

Demonstratio Mathematica

2022

Vol. 55, nr 1

470--481

This article investigates the problem of rapid exponential stabilization for nonlinear continuous systems via event-triggered impulsive control (ETIC). First, we propose a trigger mechanism that, when triggered by a predefined event, causes the closed-loop system exponentially stable. Then, the exponential stabilization is achieved by the designed ETIC with or without data dropout. The case where there are delays in the ETIC signals is also studied, and the exponential stabilization is proved. Finally, a numerical study is presented, along with numerical illustrations of the stability results.

Almost periodic synchronization of fuzzy cellular neural networks with time-varying delays via state-feedback and impulsive control

Li Yongkun, Wang Huimei, Meng Xiaofang

International Journal of Applied Mathematics and Computer Science

2019

Vol. 29, no. 2

337--349

In this paper, we are concerned with drive-response synchronization for a class of fuzzy cellular neural networks with time varying delays. Based on the exponential dichotomy of linear differential equations, the Banach fixed point theorem and the differential inequality technique, we obtain the existence of almost periodic solutions of this class of networks. Then, we design a state feedback and an impulsive controller, and construct a suitable Lyapunov function to study the problem of global exponential almost periodic synchronization for the drive-response systems considered. At the end of the paper, we provide an example to verify the effectiveness of the theoretical results.

On optimal boundary and distributed control of partial integro-differential equations

Khurshudyan A. Zh.

Archives of Control Sciences

2014

Vol. 24, no. 1

5-25

A method of optimal control problems investigation for linear partial integro-differential equations of convolution type is proposed, when control process is carried out by boundary functions and right hand side of equation. Using Fourier real generalized integral transform control problem solution is reduced to minimization procedure of chosen optimality criterion under constraints of equality type on desired control function. Optimality of control impacts is obtained for two criteria, evaluating their linear momentum and total energy. Necessary and sufficient conditions of control problem solvability are obtained for both criteria. Numerical calculations are done and control functions are plotted for both cases of control process realization.