Recurrent Model Predictive Control

TL;DR

This paper introduces Recurrent Model Predictive Control (RMPC), an off-line algorithm that uses recurrent functions to approximate optimal policies for nonlinear control problems, adapting prediction horizons dynamically and ensuring convergence to optimality.

Contribution

It presents a novel off-line RMPC algorithm employing recurrent functions for policy approximation, with proven convergence and optimality for nonlinear control tasks.

Findings

RMPC converges to the optimal policy through loss minimization.

The algorithm adapts the prediction horizon based on available computational resources.

Numerical examples demonstrate the efficiency and generality of RMPC.

Abstract

This paper proposes an off-line algorithm, called Recurrent Model Predictive Control (RMPC), to solve general nonlinear finite-horizon optimal control problems. Unlike traditional Model Predictive Control (MPC) algorithms, it can make full use of the current computing resources and adaptively select the longest model prediction horizon. Our algorithm employs a recurrent function to approximate the optimal policy, which maps the system states and reference values directly to the control inputs. The number of prediction steps is equal to the number of recurrent cycles of the learned policy function. With an arbitrary initial policy function, the proposed RMPC algorithm can converge to the optimal policy by directly minimizing the designed loss function. We further prove the convergence and optimality of the RMPC algorithm thorough Bellman optimality principle, and demonstrate its generality and efficiency using two numerical examples.