# Simultaneous state estimation and control for nonlinear systems subject to bounded disturbances

## TL;DR

This paper presents a moving horizon approach for output-feedback control of nonlinear systems with bounded disturbances, simultaneously estimating states and computing control inputs to enhance stability and robustness.

## Contribution

It introduces a novel method linking window lengths with stability, providing conditions for stabilizability and demonstrating improved performance over traditional separate estimation and control.

## Key findings

- The proposed method achieves stable control under bounded disturbances.
- Simulation results show improved accuracy and robustness.
- Linking window lengths to stability enhances control performance.

## Abstract

In this work, we address the output--feedback control problem for nonlinear systems under bounded disturbances using a moving horizon approach. The controller is posed as an optimization-based problem that simultaneously estimates the state trajectory and computes future control inputs. It minimizes a criterion that involves finite forward and backward horizon with respect the unknown initial state, measurement noises and control input variables and it is maximized with respect the unknown future disturbances. Although simultaneous state estimation and control approaches are already available in the literature, the novelty of this work relies on linking the lengths of the forward and backward windows with the closed-loop stability, assuming detectability and decoding sufficient conditions to assure system stabilizability. Simulation examples are carried out to compare the performance of simultaneous and independent estimation and control approaches as well as to show the effects of simultaneously solving the control and estimation problems.