Value Function Approximation for Nonlinear MPC: Learning a Terminal Cost Function with a Descent Property

TL;DR

This paper introduces a supervised learning approach to synthesize a terminal cost function for nonlinear MPC, enabling reduced prediction horizon and computational complexity while ensuring performance through probabilistic descent guarantees.

Contribution

The paper proposes a novel method to approximate the terminal cost function using convex function approximators with probabilistic descent guarantees, improving MPC performance and efficiency.

Findings

Reduced online computational complexity in MPC.

Probabilistic guarantees on descent condition.

Empirical validation in a numerical example.

Abstract

We present a novel method to synthesize a terminal cost function for a nonlinear model predictive controller (MPC) through value function approximation using supervised learning. Existing methods enforce a descent property on the terminal cost function by construction, thereby restricting the class of terminal cost functions, which in turn can limit the performance and applicability of the MPC. We present a method to approximate the true cost-to-go with a general function approximator that is convex in its parameters, and impose the descent condition on a finite number of states. Through the scenario approach, we provide probabilistic guarantees on the descent condition of the terminal cost function over the continuous state space. We demonstrate and empirically verify our method in a numerical example. By learning a terminal cost function, the prediction horizon of the MPC can be significantly reduced, resulting in reduced online computational complexity while maintaining good closed-loop performance.