On the Controllability of Conformable Fractional Deterministic Control Systems in Finite Dimensional Spaces

Maher Jneid,Muath Awadalla

doi:10.1155/2020/9026973

Abstract

In this paper, we establish a set of convenient conditions of controllability for semilinear fractional finite dimensional control systems involving conformable fractional derivative. Indeed, sufficient conditions of controllability for a semilinear conformable fractional system are presented, assuming that the corresponding linear systems are controllable. The present method is based on conformable fractional exponential matrix, Gramian matrix, and the iterative technique. Two illustrated examples are carried out to establish the facility and efficiency of this technique.

Highlights

Controllability concepts have played a substantial role in several fields in engineering, control theory, and applied mathematics
In 1960, the controllability was first defined by Kalman [1] as a property of shifting the systems from any initial state value into any state value at a terminal time. is definition was divided into two notions: an exact and an approximate controllability which become more suitable for dealing with control systems in infinite dimensional spaces
E purpose of those notions is the existence of control systems which are approximately controllable, but are not exact

Summary

Introduction

Controllability concepts have played a substantial role in several fields in engineering, control theory, and applied mathematics. Many researchers conducted pioneering studies in an attempt to obtain proper controllability conditions (exact and approximate) for the linear and nonlinear control systems (see, for example, [3,4,5,6,7,8] and the references cited therein). Jneid [14] derived sufficient conditions of approximate controllability for semilinear integrodifferential systems of fractional order with nonlocal conditions by using compact semigroup operator and Schauder fixedpoint theorem. Chokkalingam and Baleanu [16] obtained a set of sufficient conditions for controllability for fractional functional integrodifferential systems involving the Caputo fractional derivative of order α ∈

Preliminaries

Linear Control Systems

Semilinear Control Systems

Examples

Conclusion