Approach to design of Nonlinear Robust Control in a Class of Structurally Stable Functions

TL;DR

This paper introduces a nonlinear robust control design method using structurally stable functions from catastrophe theory, demonstrating stability and disturbance insensitivity through analytical and MATLAB simulation results.

Contribution

It presents a novel control approach employing structurally stable functions for robust stabilization of systems with wide parameter uncertainties.

Findings

Systems become stable with added controllers

Control systems are insensitive to parameter disturbances

Simulations confirm effectiveness across various examples

Abstract

An approach to stabilization of control systems with ultimately wide ranges of uncertainly disturbed parameters is offered. The method relies on using of nonlinear structurally stable functions from catastrophe theory as controllers. Analytical part presents an analysis of designed nonlinear second-order control systems. As more important the integrators in series, canonical controllable form and Jordan forms are considered. The analysis resumes that due to added controllers systems become stable and insensitive to any disturbance of parameters. Experimental part presents MATLAB simulation of design of possible control systems on the examples of epidemic spread, angular motion of aircraft and submarine depth. The results of simulation confirm the efficiency of offered method of design.