# Indirect Adaptive Fuzzy Model Predictive Control of a Rotational Inverted Pendulum

## TL;DR

This paper presents a novel indirect adaptive fuzzy model predictive control method for a nonlinear rotational inverted pendulum with uncertainties, improving tracking accuracy and stability compared to classical control approaches.

## Contribution

It introduces the first combination of Mamdani fuzzy models with model predictive control for nonlinear inverted pendulums, incorporating disturbance predictions for enhanced robustness.

## Key findings

- Significant improvement in control performance over classical MPC.
- Guaranteed stability based on Lyapunov theorem.
- Enhanced robustness to parameter variations and disturbances.

## Abstract

This paper introduces an indirect adaptive fuzzy model predictive control strategy for a nonlinear rotational inverted pendulum with model uncertainties. In the first stage, a nonlinear prediction model is provided based on the fuzzy sets, and the model parameters are tuned through the adaption rules. In the second stage, the model predictive controller is designed based on the predicted inputs and outputs of the system. The control objective is to track the desired outputs with minimum error and to maintain closed-loop stability based on the Lyapunov theorem. Combining the adaptive Mamdani fuzzy model with the model predictive control method is proposed for the first time for the nonlinear inverted pendulum. Moreover, the proposed approach considers the disturbances predictions as part of the system inputs which have not been considered in the previous related works. Thus, more accurate predictions resistant to the parameters variations enhance the system performance using the proposed approach. A classical model predictive controller is also applied to the plant, and the results of the proposed strategy are compared with the results from the classical approach. Results proved that the proposed algorithm improves the control performance significantly with guaranteed stability and excellent tracking. Keywords: Indirect adaptive fuzzy; Model predictive control; Nonlinear rotational inverted pendulum; Model uncertainties; Lyapunov stability theorem.