Barrier Integral Control for Global Asymptotic Tracking of Uncertain Nonlinear Systems under State and Input Constraints

TL;DR

This paper introduces Barrier Integral Control (BRIC), a novel control algorithm for uncertain nonlinear systems that guarantees state constraint adherence and asymptotic tracking without requiring knowledge of system dynamics.

Contribution

The paper presents BRIC, a new control method that ensures constraint satisfaction and asymptotic tracking for uncertain nonlinear systems without relying on dynamic information or bounds.

Findings

BRIC effectively enforces state constraints during tracking.

The algorithm achieves asymptotic convergence from any initial condition.

Simulation results demonstrate superior performance over existing methods.

Abstract

This paper addresses the problem of asymptotic tracking for high-order control-affine MIMO nonlinear systems with unknown dynamic terms subject to input and transient state constraints. We introduce Barrier Integral Control (BRIC), a novel algorithm designed to confine the system's state within a predefined funnel, ensuring adherence to the transient state constraints, and asymptotically drive it to a given reference trajectory from any initial condition. The algorithm leverages the innovative integration of a reciprocal barrier function and error-integral terms, featuring smooth feedback control. We further develop an extension of the algorithm, entailing continuous feedback, that uses a reference-modification technique to account for the input-saturation constraints. Notably, BRIC operates without relying on any information or approximation schemes for the (unknown) dynamic terms, which, unlike a large class of previous works, are not assumed to be bounded or to comply with globally Lipschitz/growth conditions. Additionally, the system's trajectory and asymptotic performance are decoupled from the uncertain model, control-gain selection, and initial conditions. Finally, comparative simulation studies validate the effectiveness of the proposed algorithm.