Control of Unknown (Linear) Systems with Receding Horizon Learning

TL;DR

This paper introduces a receding horizon learning approach for stabilizing unknown linear systems using only input-output data, with proven convergence and demonstrated effectiveness through simulations.

Contribution

It presents a novel model-free control scheme combining receding horizon control and proximity-based estimation for unknown linear systems.

Findings

Proven global convergence to zero for stabilizable systems.

Effective control demonstrated in simulations for linear and nonlinear systems.

No prior system model required, only input-output data and an upper bound on state dimension.

Abstract

A receding horizon learning scheme is proposed to transfer the state of a discrete-time dynamical control system to zero without the need of a system model. Global state convergence to zero is proved for the class of stabilizable and detectable linear time-invariant systems, assuming that only input and output data is available and an upper bound of the state dimension is known. The proposed scheme consists of a receding horizon control scheme and a proximity-based estimation scheme to estimate and control the closed-loop trajectory. Simulations are presented for linear and nonlinear systems.