Explicit Reference Governor for Continuous Time Nonlinear Systems Subject to Convex Constraints

TL;DR

This paper presents a new explicit reference governor method for continuous-time nonlinear systems that ensures convex constraint satisfaction by dynamically adjusting the reference based on Lyapunov functions.

Contribution

It introduces a closed-form, Lyapunov-based reference modulation strategy applicable to general nonlinear systems with convex constraints, including explicit solutions for polyhedral cases.

Findings

Explicit solution for polyhedral constraints in nonlinear systems.

Enhanced control performance for linear systems and robotic manipulators.

Theoretical guarantees of constraint satisfaction via Lyapunov function modulation.

Abstract

This paper introduces a novel closed-form strategy that dynamically modifies the reference of a pre-compensated nonlinear system to ensure the satisfaction of a set of convex constraints. The main idea consists of translating constraints in the state space into constraints on the Lyapunov function and then modulating the reference velocity so as to limit the value of the Lyapunov function. The theory is introduced for general nonlinear systems subject to convex constraints. In the case of polyhedric constraints, an explicit solution is provided for the large and highly relevant class of nonlinear systems whose Lyapunov function is lower-bounded by a quadratic form. In view of improving performances, further specializations are provided for the relevant cases of linear systems and robotic manipulators.