Data-Driven Tube-Based Zonotopic Predictive Control With Nonconvex Layered Terminal Sets

TL;DR

This paper introduces a novel data-driven tube-based zonotopic predictive control framework utilizing layered nonconvex terminal sets to improve feasibility and reduce conservatism in control design.

Contribution

It proposes a layered terminal-set design and a data-driven characterization of the inverse model set, enhancing stability certification and feasibility in DTZPC.

Findings

Tighter inverse-set enclosures achieved.

Enhanced feasibility over existing schemes.

Numerical examples demonstrate improved control performance.

Abstract

This paper presents a data-driven tube-based zonotopic predictive control (DTZPC) framework with nonconvex layered terminal sets. Existing DTZPC schemes with closed-loop guarantees typically rely on a single ellipsoidal terminal set, which can be conservative and thereby limit feasibility. We propose a layered terminal-set design that decouples stability certification, feasibility enlargement, and motion-region screening into three components with distinct roles. First, an offline-designed feedback gain together with a contractive constrained zonotope provides a terminal ingredient for stability certification, while avoiding probabilistic feedback synthesis in high-dimensional DTZPC. Second, we derive a data-driven characterization of the inverse admissible closed-loop model set, avoiding the conservatism of interval-matrix relaxation and inversion. Combined with exact set multiplication, this yields inner and outer approximations of the maximal robust positively invariant (MRPI) set under fixed closed-loop dynamics. The inner approximation serves as a nonconvex terminal set to enlarge feasibility, whereas the outer approximation provides certified motion-region descriptions for fast screening and monitoring. Numerical examples demonstrate tighter inverse-set enclosures and improved feasibility over existing convex-terminal DTZPC schemes.