Exploiting Over-Approximation Errors as Preview Information for Nonlinear Control

TL;DR

This paper introduces a novel approach to nonlinear control by leveraging over-approximation errors as preview information, enabling the design of informed policies that improve control accuracy.

Contribution

It formulates the concretization problem as a fixed-point equation and provides efficient computational methods for both input-affine and nonlinear systems.

Findings

Over-approximation errors can be exploited as preview information.

Existence of solutions is guaranteed by Brouwer's fixed-point theorem.

Efficient algorithms are developed for different system types.

Abstract

We study the control of nonlinear constrained systems via over-approximations. Our key observation is that the over-approximation error, rather than being an unknown disturbance, can be exploited as input-dependent preview information. This leads to the notion of informed policies, which depend on both the state and the error. We formulate the concretization problem -- recovering a valid input for the true system from a preview-based policy -- as a fixed-point equation. Existence of solutions follows from the Brouwer fixed-point theorem, while efficient computation is enabled through closed-form, linear, or convex programs for input-affine systems, and through an iterative method based on the Banach fixed-point theorem for nonlinear systems.