# Unifying Controller Design for Stabilizing Nonlinear Systems with Norm-Bounded Control Inputs

arXiv: https://arxiv.org/abs/2403.03030 · HTML: https://mlsanity.com/paper/2403.03030/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 30 references that are in the map.
- First posted on arXiv 5 Mar 2024.

## Builds on (most cited first, 7 of 7)

- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Regularity Properties of Optimization-Based Controllers](https://mlsanity.com/paper/2311.13167/) (2023)
- [Inverse Optimal Safety Filters](https://mlsanity.com/paper/2112.08225/) (2021)
- [Stabilization of affine systems with polytopic control value sets](https://mlsanity.com/paper/2112.02451/) (2021)
- [Quadrotor Stabilization with Safety Guarantees: A Universal Formula Approach](https://mlsanity.com/paper/2401.03500/) (2024)
- [Chetaev Instability Framework for Kinetostatic Compliance-Based Protein Unfolding](https://mlsanity.com/paper/2205.07375/) (2022)
- [Characterizing Smooth Safety Filters via the Implicit Function Theorem](https://mlsanity.com/paper/2309.12614/) (2023)

## Abstract (arXiv)

This paper revisits a classical challenge in the design of stabilizing controllers for nonlinear systems with a norm-bounded input constraint. By extending Lin-Sontag's universal formula and introducing a generic (state-dependent) scaling term, a unifying controller design method is proposed. The incorporation of this generic scaling term gives a unified controller and enables the derivation of alternative universal formulas with various favorable properties, which makes it suitable for tailored control designs to meet specific requirements and provides versatility across different control scenarios. Additionally, we present a constructive approach to determine the optimal scaling term, leading to an explicit solution to an optimization problem, named optimization-based universal formula. The resulting controller ensures asymptotic stability, satisfies a norm-bounded input constraint, and optimizes a predefined cost function. Finally, the essential properties of the unified controllers are analyzed, including smoothness, continuity at the origin, stability margin, and inverse optimality. Simulations validate the approach, showcasing its effectiveness in addressing a challenging stabilizing control problem of a nonlinear system.