# Lyapunov-based Model Reference Adaptive Controller Design for a Class of Nonlinear Fractional Order Systems

## TL;DR

This paper develops a Lyapunov-based adaptive control method for nonlinear fractional order systems, addressing the challenge of stability analysis without the chain rule, and demonstrates effectiveness through numerical simulations.

## Contribution

It introduces a direct Lyapunov-based adaptive control approach for nonlinear fractional systems, overcoming limitations of existing indirect methods that rely on frequency distributed models.

## Key findings

- Controller achieves stable tracking in simulations
- Lyapunov stability is proven using fractional inequalities
- Method outperforms traditional indirect approaches

## Abstract

This paper is concerned with model reference adaptive controller design for a class of nonlinear fractional order systems. Recent works on this topic rarely include direct methods and they are mostly based on indirect methods where the frequency distributed model is used to prove the stability of the closed loop system. Since the chain rule cannot be applied in fractional derivations, in order to prove the lyapunov stability here fractional inequalities are used. Finally, by means of a numerical example, the controller performance is demonstrated.

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Source: https://tomesphere.com/paper/1706.01736