Controllability of nonlinear systems with delay in control

In this paper we study the relative controllability of nonlinear neutral system with distributed and multiple lumped time varying delays in control. Using Schauder's fixed point theorem sufficient conditions for relative controllability in a given time interval are formulated and proved. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 565-570

Sufficient conditions for global controllability of certain types of perturbed nonlinear time-varying systems are given. The results are obtained by using Schauder's fixed-point theorem.

Null controllability of nonlinear infinite neutral systems with delays in control

Sufficient conditions are developed for the relative controllability of nonlinear neutral systems with time-varying multiple delays in both state and control. The results are obtained by using Schauder's fixed-point theorem Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 559-564

In this paper, we discuss the controllability of fractional Langevin delay dynamical systems represented by the fractional delay differential equations of order 0 < α,β ≤ 1. Necessary and sufficient conditions for the controllability of linear fractional Langevin delay dynamical system are obtained by using the Grammian matrix. Sufficient conditions for the controllability of the nonlinear delay dynamical systems are established by using the Schauders fixed-point theorem. The problem of controllability of linear and nonlinear fractional Langevin delay dynamical systems with multiple delays and distributed delays in control are studied by using the same technique. Examples are provided to illustrate the theory.

Sufficient conditions for global relative controllability of nonlinear systems with time-varying multiple delays in control and implicit derivatives are derived. The special case, when the delays are constant, is also considered and an example is provided. The results are obtained using the measure of noncompactness of a set and Darbo's fixed-point principle.

A new approach using graph-theory to determine the controllability and observability of large scale nonlinear dynamic thermal systems is presented. The novelty of this method is in adapting graph theory for a nonlinear class and establishing graphic conditions that describe the necessary and sufficient conditions for a class of nonlinear systems to be controllable and observable which is equivalent to the analytical method of Lie algebra rank condition. Graph theory of directed graph (digraph) is utilized to model the system and its adaptation to nonlinear problems is defined. The necessary and sufficient conditions for controllability are investigated through the structural property of a digraph called connectability. In comparison to the Lie Algebra, this approach has proven to be easier, from a computational point of view, thus it is found to be useful when dealing with large scale systems. This paper presents the problem statement, properties of structured system, and analytical method of Lie algebra rank condition for controllability and observability of bilinear systems. The main results of graphical approach which describe the necessary and sufficient conditions for controllability of nonlinear systems are presented and applied to the problem of a coupled two heat exchangers, connected in an arbitrary fashion.

In the present paper finite-dimensional dynamical control systems described by linear higherorder ordinary differential state equations with multiple point delays in control are considered. Using algebraic methods, necessary and sufficient condition for relative controllability in a given time interval for linear dynamical system with multiple point delays in control is formulated and proved. This condition is generalization to relative controllability case some previous results concerning controllability of linear dynamical systems without multiple point delays in the control. Simple numerical example, which illustrates theoretical result is also given. Finally, some remarks and comments on the existing results for controllability of dynamical systems with delays in control are also presented.

Sufficient conditions for the local null controllability of non-linear functional differential systems with unbounded linear operators in Banach space are established. The results are obtained using the semigroup of linear operators, fractional powers of operators, and the Schauder fixed-point theorem. Applications to parabolic differential systems are given.

This study explores their utility in solving nonlinear integral equations, a class of equations frequently encountered in mathematical modeling of physical, biological, and engineering systems.We provide a comprehensive review of key fixed-point theorems, including Banach's Contraction Principle, Schauder's Fixed-Point Theorem, and their generalizations.Emphasis is placed on the conditions under which these theorems can be applied to nonlinear integral equations.Examples demonstrate the practical implementation of these theorems to guarantee the existence and uniqueness of solutions.The results highlight the interplay between the structure of metric spaces, operator properties, and the formulation of integral equations, offering a robust framework for tackling nonlinear problems across diverse applications.

Third-order systems: Periodicity conditions

The sufficient conditions for existence and partial approximate controllability of fractional stochastic evolution equations with nonlocal initial conditions have been discussed. The discussion is based on the variational method, fractional calculus, Schauder's fixed point theorem, and stochastic analysis. Contrary to the results available in the literature, the non-local function does not need to be compact or satisfy Lipschitz's condition. Moreover, the pertinent nonlinear function does not need to be uniformly bounded. At the end, an application has also been demonstrated.

Stability analysis of a CALM floating offshore structure

The Sufficient Condition for the Approximate Controllability of Nonlinear Abstract Control System

In this paper, a reaction-diffusion model with a cyclic structure is studied, which includes the SIS disease-transmission model and the nutrient-phytoplankton model. The minimal wave speed $ c^* $ of traveling wave solutions is given. The existence of traveling semi-fronts with $ c>c^* $ is proved by Schauder's fixed-point theorem. The traveling semi-fronts are shown to be bounded by rescaling method and comparison principle. The existence of traveling semi-front with $ c = c^* $ is obtained by limit arguments. Finally, the traveling semi-fronts are shown to connect to the positive equilibrium by a Lyapunov function.