# Adaptive sliding mode control without knowledge of uncertainty bounds

## TL;DR

This paper introduces an adaptive sliding mode control method for nonlinear systems with unknown, time-varying uncertainties, eliminating the need for prior uncertainty bounds and reducing chattering.

## Contribution

It presents a novel adaptation law that adjusts control gains without prior uncertainty bounds, ensuring stability and improved control performance.

## Key findings

- Reduces control gain magnitude to minimum
- Smooths out chattering in control signals
- Ensures semi-global stability of the system

## Abstract

This paper proposes a new adaptation methodology to find the control inputs for a class of nonlinear systems with time-varying bounded uncertainties. The proposed method does not require any prior knowledge of the uncertainties including their bounds. The main idea is developed under the structure of adaptive sliding mode control; an update law decreases the gain inside and increases the gain outside a vicinity of the sliding surface. The semi-global stability of the closed-loop system and the adaptation error are guaranteed by Lyapunov theory. The simulation results show that the proposed adaptation methodology can reduce the magnitude of the controller gain to the minimum possible value and smooth out the chattering.