Approximate Controllabilty of Semilinear Dynamic Equations on Time Scale

In this paper, we investigate the analysis of reachability and controllability for time‐varying linear systems evolving on nonuniform time domains also known as arbitrary time scales. Based on appropriate operators, some necessary and sufficient conditions are derived to guarantee the reachability for this class of systems using linear algebra tools. Furthermore, a link between optimality and the proposed operators is given. Then, the connection between reachability and controllability analysis on arbitrary time scales is discussed. Through the paper, some examples illustrate the theoretical results.

Section: Problem Formulationmentioning

confidence: 99%

Time scale reachability and controllability of time‐varying linear systems

Nasser

Djemaï

Defoort

et al. 2021

“…In Xie and Wang [16], the authors extended the results of Wei and Song [15] to multiple time‐delayed cases. Further, the controllability results of dynamic systems on time scales is a relatively newer area and only a few works have been reported [19–26] and references therein. Particularly, in Davis et al [19], the authors considered a non‐singular dynamical system on time scales

\begin{matrix} alignleft \\ align-1 x^{Δ} (t) & align-2 = A x (t) + B u (t), \\ align-1 x (t_{0}) & align-2 = x_{0} \end{matrix}

and established the controllability and observability results.…”

Section: Introductionmentioning

confidence: 99%

Controllability of singular dynamic systems on time scales

Malik

Sajid²,

Kumar

2021

In this work, we investigate the controllability of singular dynamic systems on time scales. First, we decompose the consider systems into a slow subsystem and a fast subsystem. After that, we use the Laplace transform and convolution theorem to derive the state response of these two subsystems. Finally, we established some necessary and sufficient conditions for the controllability of the slow subsystem and fast subsystem. At last, we provide an example to illustrate the obtained analytical results.

“…The significance of the approximate controllability lies in the fact that an arbitrary initial state can be steered toward an arbitrarily small neighborhood of any given target state by choosing a control function in the appropriate way. To get points of interest about this, one can see [18‐25] and the references cited therein. Research investigating trajectory controllability was started in 1996 by Raju K. George.…”

Section: Introductionmentioning

confidence: 99%

Approximate and trajectory controllability of fractional stochastic differential equation with non‐instantaneous impulses and Poisson jumps

Dhayal

Malik

Abbas

2020

The problem of approximate controllability is investigated in this paper for a class of fractional stochastic differential equations driven by fractional Brownian motion with non‐instantaneous impulses and Poisson jumps. The results are obtained by employing the η‐resolvent family and Krasnoselskii's fixed point theorem. Further, we derive the trajectory controllability for the proposed stochastic control system. Finally, an example is provided to illustrate the obtained theory.