Impulsive Control of Some Types of Nonlinear Systems Using a Set of Uncertain Control Matrices

Abstract

So many real life problems ranging from medicine, agriculture, biology and finance are modelled by nonlinear systems. In this case, a chaotic nonlinear system is considered and, as opposed to solving Linear Matrix Inequality (LMI), which is the usual approach but cumbersome, a completely different approach was used. In some other cases, the computation of singular value of matrix was used but the method in this study needs not such. In addition, most models, if not all, concentrate on finding a control matrix J under some sufficient conditions. The problem is that only one such matrix J is provided. In reality, the actual control quantity may have a little deviation from the theoretical J. Hence, the study in this paper provides a set of infinite uncertain matrices Jα which are able to adapt to control the system under uncertain conditions. It turns out that this new method controls the system in shorter time with less computational complexities.

Well-Posedness, Dynamics, and Control of Nonlinear Differential System with Initial-Boundary Value

“…The objective of [5] is to provide a set of infinite uncertainty matrices J α that can adapt to control systems under uncertain conditions. The numerical simulation results illuminate that the new method can control the system in a short time and has low computational complexity.…”

“…The series of papers in this Special Issue reflect the application of dynamic system theory in finance, neural networks, and other control systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. For example, the authors of [1] studied the stability of PSS in hyperchaotic financial systems.…”

“…The stability criterion of the financial system in [1] has a large pulse allowable range, and does not limit that the pulse must be less than 1, thus reducing conservatism, which is common in the actual financial market, that is, investors and financial management departments have difficulty ensuring whether their impulsive measures are conducive to the stability of the financial system, while the impulsive stability criterion in [1] is more suitable for guiding the impulsive stability plan in the actual financial engineering. Next, the mathematical model in [5] involves nonlinear system modeling in medicine, agriculture and biology. In addition, the authors of [6] used a direct analysis method to study the asymptotic stability and synchronization of a fractional order complex valued inertial neural network.…”

“…On the other hand, the stability and synchronization control of dynamic systems are also among the main contents of cybernetics, and they are part of well-posed problems. Fifteen papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14] in this Special Issue deal with the stabilization and synchronization control of initial boundary value problems of partial differential equations or ordinary differential equations, and jointly complete the original work plan of this Special Issue. The papers in this Special Issue can be divided according to the following scheme considering their main purposes:…”