Learning the cost-to-go for mixed-integer nonlinear model predictive control

TL;DR

This paper introduces an approximate mixed-integer nonlinear model predictive control method that reduces online computation by offline value function approximation, enabling real-time control of hybrid systems.

Contribution

It proposes a novel approach combining offline value function approximation with a shortened online horizon for mixed-integer NMPC, improving real-time feasibility.

Findings

Reduced online computation for mixed-integer NMPC

Effective approximation of the value function offline

Successful demonstration on an inverted pendulum example

Abstract

Application of nonlinear model predictive control (NMPC) to problems with hybrid dynamical systems, disjoint constraints, or discrete controls often results in mixed-integer formulations with both continuous and discrete decision variables. However, solving mixed-integer nonlinear programming problems (MINLP) in real-time is challenging, which can be a limiting factor in many applications. To address the computational complexity of solving mixed integer nonlinear model predictive control problem in real-time, this paper proposes an approximate mixed integer NMPC formulation based on value function approximation. Leveraging Bellman's principle of optimality, the key idea here is to divide the prediction horizon into two parts, where the optimal value function of the latter part of the prediction horizon is approximated offline using expert demonstrations. Doing so allows us to solve the MINMPC problem with a considerably shorter prediction horizon online, thereby reducing the online computation cost. The paper uses an inverted pendulum example with discrete controls to illustrate this approach.