Set-Based State Estimation of Nonlinear Discrete-Time Systems Using Constrained Zonotopes and Polyhedral Relaxations
- Authors: Brenner S. Rego, Guilherme V. Raffo, Marco H. Terra, Joseph K. Scott
- Source: arXiv:2504.00130 (March 2025)
- Constrained zonotopes are used as the set representation. Constrained zonotopes generalize ordinary zonotopes by adding linear constraints, making them strictly more expressive while retaining efficient set operations.
- Polyhedral relaxations of the nonlinear dynamics are used to propagate the state enclosure through the nonlinear discrete-time equations, yielding guaranteed outer approximations.
Overview
This work studies set-based state estimation for nonlinear discrete-time systems. Instead of producing a single point estimate, set-based (guaranteed) estimation computes an enclosure of all states consistent with the system model, bounded process noise, and measurement noise.
Key Ideas
Why It Matters
Guaranteed state enclosures are useful in robust control, safety-critical systems, verification, and fault detection, where bounds on estimation error must be rigorous rather than probabilistic.
Note on This Forum Post
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