Polytopic Input Constraints in Learning-Based Optimal Control Using Neural Networks

TL;DR

This paper introduces two neural network-based methods for handling polytopic input constraints in discrete-time optimal control, enabling constraint satisfaction and improved control performance.

Contribution

It presents novel approaches using gradient-based and softmax output neural networks to incorporate input constraints in model predictive control.

Findings

Gradient method with closed-form derivatives effectively enforces constraints.

Softmax neural networks provide a convex combination approach for input constraints.

Numerical examples demonstrate the practical applicability of both methods.

Abstract

This work considers artificial feed-forward neural networks as parametric approximators in optimal control of discrete-time systems. Two different approaches are introduced to take polytopic input constraints into account. The first approach determines (sub-)optimal inputs by the application of gradient methods. Closed-form expressions for the gradient of general neural networks with respect to their inputs are derived. The approach allows to consider state-dependent input constraints, as well as to ensure the satisfaction of state constraints by exploiting recursive reachable set computations. The second approach makes use of neural networks with softmax output units to map states into parameters, which determine (sub-)optimal inputs by a convex combination of the vertices of the input constraint set. The application of both approaches in model predictive control is discussed, and results obtained for a numerical example are used for illustration.