Exponentially Convergent Direct Adaptive Pole Placement Control of Plants with Unmatched Uncertainty under FE Condition

TL;DR

This paper introduces a novel direct adaptive pole placement control method for plants with unmatched uncertainty, ensuring exponential stability and convergence without needing prior control input matrix information.

Contribution

It presents a new APPC scheme that guarantees exponential stability and parameter convergence under FE conditions, without requiring a priori control input matrix knowledge.

Findings

Guarantees exponential stability of the control system.

Ensures exponential convergence of control law parameters.

Supports theoretical results with numerical experiments.

Abstract

A new method of direct adaptive pole placement control (APPC) is developed for plants with unmatched uncertainty, which linearly depends on a state vector. It guarantees the exponential stability of a control system and exponential convergence of control law adjustable parameters to their true values when the regressor is finitely exciting. Considering the known classical APPC schemes and adaptive methods with exponential regulation, the advantages of the proposed one are that it does not require a priori information on a control input matrix and ensures the monotonic transient behavior of each adjustable parameter of the control law. The theoretical results are supported by the numerical experiments.