Robust Global Adaptive Exponential Stabilization of Discrete-Time Systems with Application to Freeway Traffic Control

TL;DR

This paper develops an adaptive control method for uncertain discrete-time systems, ensuring robust, global, exponential stability, with practical application demonstrated on freeway traffic models.

Contribution

It introduces a novel adaptive control scheme combining a nominal feedback law with a dead-beat observer for uncertain discrete-time systems.

Findings

Achieves robust, global, exponential stability in uncertain systems.

Successfully applied to freeway traffic control models.

Demonstrates effectiveness in highly nonlinear, uncertain environments.

Abstract

This paper is devoted to the development of adaptive control schemes for uncertain discrete-time systems, which guarantee robust, global, exponential convergence to the desired equilibrium point of the system. The proposed control scheme consists of a nominal feedback law, which achieves robust, global, exponential stability properties when the vector of the parameters is known, in conjunction with a nonlinear, dead-beat observer. The obtained results are applicable to highly nonlinear, uncertain discrete-time systems with unknown constant parameters. The applicability of the obtained results to real control problems is demonstrated by the rigorous application of the proposed adaptive control scheme to uncertain freeway models.