Control of Nonlinear Systems Under Multiple Time-Varying Output Constraints: A Single Funnel Approach

TL;DR

This paper introduces a unified funnel control method for uncertain nonlinear systems with multiple, coupled, time-varying output constraints, ensuring constraint satisfaction and system stability.

Contribution

It presents a novel single funnel approach that simplifies handling multiple output constraints into a scalar condition, improving robustness and reducing complexity.

Findings

Successfully verified through simulation example.

Ensures convergence and invariance of output constraints.

Provides a robust, low-complexity control design.

Abstract

This paper proposes a novel control framework for handling (potentially coupled) multiple time-varying output constraints for uncertain nonlinear systems. First, it is shown that the satisfaction of multiple output constraints boils down to ensuring the positiveness of a scalar variable (the signed distance from the time-varying output-constrained set's boundary). Next, a single funnel constraint is designed properly, whose satisfaction ensures convergence to and invariance of the time-varying output-constrained set. Then a robust and low-complexity funnel-based feedback controller is designed employing the prescribed performance control method. Finally, a simulation example clarifies and verifies the proposed approach.