# Families of Control-Cost-Parametrized Inverse-Optimal Universal Stabilizers

arXiv: https://arxiv.org/abs/2606.09047 · HTML: https://mlsanity.com/paper/2606.09047/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 41 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Builds on (most cited first, 14 of 14)

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- [Neural Operators for Boundary Stabilization of Stop-and-go Traffic](https://mlsanity.com/paper/2312.10374/) (2023)
- [Backstepping Neural Operators for 2× 2 Hyperbolic PDEs](https://mlsanity.com/paper/2312.16762/) (2023)
- [Operator Learning for Robust Stabilization of Linear Markov-Jumping Hyperbolic PDEs](https://mlsanity.com/paper/2412.09019/) (2024)
- [A Complete Inverse Optimality Study for a Tank-Liquid System](https://mlsanity.com/paper/2405.16535/) (2024)
- [Inverse optimal design of input-to-state stabilizing homogeneous controllers for nonlinear homogeneous systems](https://mlsanity.com/paper/2511.15034/) (2025)
- [Nonholonomic Robot Parking by Feedback -- Part I: Modular Strict CLF Designs](https://mlsanity.com/paper/2511.15119/) (2025)
- [Contractor-Expander and Universal Inverse Optimal Positive Nonlinear Control](https://mlsanity.com/paper/2603.02530/) (2026)
- [Neural Operators for Multi-Task Control and Adaptation](https://mlsanity.com/paper/2604.03449/) (2026)
- [FNOangle θ: Extended Fourier neural operator for learning state and optimal control of distributed parameter systems](https://mlsanity.com/paper/2604.05187/) (2026)

## Abstract (arXiv)

A classical universal stabilization formula offers the practitioner no design freedom: it is a single, parameter-free object. We introduce a cost-parametrized family of stabilizing feedback laws, where (1) the user chooses a function that serves as the running cost on control in an inverse-optimal cost functional, and (2) obtains, through a formula, a nonlinear "expander" of a pre-existing universal controller, which solves an infinite-horizon optimal control problem with a meaningful cost on the state. The cost-to-expander formula is a three-step construction, involving, inter alia, cost differentiation and function inversion-overall, a nonlinear infinite-dimensional operator. The cost-to-expander operator is proven Lipschitz, which enables uniform neural operator approximation of the entire family and supports both offline performance exploration and online adaptation. Semiglobal practical asymptotic stability and second-order suboptimality bounds are established under the approximation. The operator learning and its use in semiglobal stabilization are illustrated numerically. We call the result 'half-direct-optimal' because the paper's design is less than a general 'direct optimal' (HJB-inducing) control, but more than the fully inverse optimal, since the user performs minimization for an arbitrary given cost on control. The dual to the half-direct problem we solve is the problem in which the cost on the state is arbitrary and given. This dual problem is easier and outside of the scope of the paper.