# Input Influence Matrix Design for MIMO Discrete-Time Ultra-Local Model

arXiv: https://arxiv.org/abs/2203.08729 · HTML: https://mlsanity.com/paper/2203.08729/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Mar 2022.

## Built on by (most cited first, 2 of 2)

- [CHyLL: Learning Continuous Neural Representations of Hybrid Systems](https://mlsanity.com/paper/2512.10117/) (2025)
- [Learning Continuous Neural Representation of Stochastic Hybrid Systems](https://mlsanity.com/paper/2609.38893/) (2026)

## Abstract (arXiv)

Ultra-Local Models (ULM) have been applied to perform model-free control of nonlinear systems with unknown or partially known dynamics. Unfortunately, extending these methods to MIMO systems requires designing a dense input influence matrix which is challenging. This paper presents guidelines for designing an input influence matrix for discrete-time, control-affine MIMO systems using an ULM-based controller. This paper analyzes the case that uses ULM and a model-free control scheme: the H"older-continuous Finite-Time Stable (FTS) control. By comparing the ULM with the actual system dynamics, the paper describes how to extract the input-dependent part from the lumped ULM dynamics and finds that the tracking and state estimation error are coupled. The stability of the ULM-FTS error dynamics is affected by the eigenvalues of the difference (defined by matrix multiplication) between the actual and designed input influence matrix. Finally, the paper shows that a wide range of input influence matrix designs can keep the ULM-FTS error dynamics (at least locally) asymptotically stable. A numerical simulation is included to verify the result. The analysis can also be extended to other ULM-based controllers.