Function Approximation Technique Based Immersion and Invariance Control for Unknown Nonlinear Systems

A function approximation technique based immersion and invariance (FATII) control method is proposed in this letter. Firstly, an unknown control system is restructured as the combination of an auxiliary system and a variation term from the original system. The variation term is treated as a time-varying uncertainty and parameterized by a group of weighted chosen basis functions. These weights are estimated at every time instant and the change of the estimates is governed by an update law. The update law is defined based on an immersion and invariance approach such that both the system state and the estimation error converge to zero. The FATII method is model-free and thus applicable to a wide range of systems. The asymptotic stability of the proposed method is established and its feasibility is verified under simulations.

I. Introduction

The need for the control of nonlinear systems arises in many practical applications that include the use of ships, underwater vehicles, aircraft, satellites, flexible joint robots, hyper-redundant and snake-like manipulators, walking robots, hybrid machines, etc.