arXiv subjects

Jonah J. Glunt

Publications and source records attributed to Jonah J. Glunt.

9 recordsLinked to original sources

arXiv2026

Moving Horizon Estimation of Hybrid Systems Using Hybrid Zonotopes and Mixed-Integer Quadratic Programs

Moving horizon estimation (MHE) is an estimation technique that formulates an optimization problem over a past horizon to find the states that require the minimum disturbances and noise to be feasible with the dynamics and measurements. For hybrid systems with both continuous and discrete states, this yields a mixed-integer program for the MHE, which can be difficult both to formulate and solve online under computational limitations. This paper shows how the hybrid zonotope representation for mixed-integer sets can be used to efficiently construct the feasible space for the program using reachability-based calculations for piecewise affine systems, without requiring conversion to a mixed logical dynamical system. A method for lifting the state space to explicitly estimate the dynamic mode is also presented. The proposed approach is evaluated in two numerical examples. Comparison against a standard mixed logical dynamical systems approach shows the proposed method can be solved orders of magnitude faster for one of the example problems.

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arXiv2026

Hybrid System Planning using a Mixed-Integer ADMM Heuristic and Hybrid Zonotopes

Embedded optimization-based planning for hybrid systems is challenging due to the use of mixed-integer programming, which is computationally intensive and often sensitive to the specific numerical formulation. To address that challenge, this article proposes a framework for motion planning of hybrid systems that pairs hybrid zonotopes - an advanced set representation - with a new alternating direction method of multipliers (ADMM) mixed-integer programming heuristic. A general treatment of piecewise affine (PWA) system reachability analysis using hybrid zonotopes is presented and extended to formulate optimal planning problems. Sets produced using the proposed identities have lower memory complexity and tighter convex relaxations than equivalent sets produced from preexisting techniques. The proposed ADMM heuristic makes efficient use of the hybrid zonotope structure. For planning problems formulated as hybrid zonotopes, the proposed heuristic achieves improved convergence rates as compared to state-of-the-art mixed-integer programming heuristics. The proposed methods for hybrid system planning on embedded hardware are experimentally applied in a combined behavior and motion planning scenario for autonomous driving.

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arXiv2026

Shared Situational Awareness Using Hybrid Zonotopes with Confidence Metric

Situational awareness for connected and automated vehicles describes the ability to perceive and predict the behavior of other road-users in the near surroundings. However, pedestrians can become occluded by vehicles or infrastructure, creating significant safety risks due to limited visibility. Vehicle-to-everything communication enables the sharing of perception data between connected road-users, allowing for a more comprehensive awareness. The main challenge is how to fuse perception data when measurements are inconsistent with the true locations of pedestrians. Inconsistent measurements can occur due to sensor noise, false positives, or unmodeled disturbances. This paper employs set-based estimation with constrained zonotopes to compute a confidence metric for the measurement set from each sensor. Estimated sets and their confidences are then fused using hybrid zonotopes. This method can account for inconsistent measurements, enabling reliable and robust fusion of the sensor data. The effectiveness of the proposed method is demonstrated in both simulation and real experiments.

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arXiv2026

Motion Planning with Metric Temporal Logic Using Reachability Analysis and Hybrid Zonotopes

Metric temporal logic (MTL) provides a formal framework for defining time-dependent mission requirements on autonomous vehicles. However, optimizing control decisions subject to these constraints is often computationally expensive. This article presents a method that uses reachability analysis to implicitly express the set of states satisfying an MTL specification and then optimizes to find a motion plan. The hybrid zonotope set representation is used to efficiently and conveniently encode MTL specifications into reachable sets. A numerical benchmark highlights the proposed method's computational advantages as compared to existing methods in the literature. Further numerical examples and an experimental application demonstrate the ability to address time-varying environments, region-dependent disturbances, and multi-agent coordination.

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arXiv2025

Sharp Hybrid Zonotopes: Set Operations and the Reformulation-linearization Technique

Mixed integer set representations, and specifically hybrid zonotopes, have enabled new techniques for reachability and verification of nonlinear and hybrid systems. Mixed-integer sets which have the property that their convex relaxation is equal to their convex hull are said to be sharp. This property allows the convex hull to be computed with minimal overhead, and is known to be important for improving the convergence rates of mixed-integer optimization algorithms that rely on convex relaxations. This paper examines methods for formulating sharp hybrid zonotopes and provides sharpness-preserving methods for performing several key set operations. The paper then shows how the reformulation-linearization technique can be applied to create a sharp realization of a hybrid zonotope that is initially not sharp. A numerical example applies this technique to find the convex hull of a level set of a feedforward ReLU neural network.

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arXiv2025

Automated Functional Decomposition for Hybrid Zonotope Over-approximations with Application to LSTM Networks

Functional decomposition is a powerful tool for systems analysis because it can reduce a function of arbitrary input dimensions to the sum and superposition of functions of a single variable, thereby mitigating (or potentially avoiding) the exponential scaling often associated with analyses over high-dimensional spaces. This paper presents automated methods for constructing functional decompositions used to form set-based over-approximations of nonlinear functions, with particular focus on the hybrid zonotope set representation. To demonstrate these methods, we construct a hybrid zonotope set that over-approximates the input-output graph of a long short-term memory neural network, and use functional decomposition to represent a discrete hybrid automaton via a hybrid zonotope.

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arXiv2024

Error Bounds for Compositions of Piecewise Affine Approximations

Nonlinear expressions are often approximated by piecewise affine (PWA) functions to simplify analysis or reduce computational costs. To reduce computational complexity, multivariate functions can be represented as compositions of functions with one or two inputs, which can be approximated individually. This paper provides efficient methods to generate PWA approximations of nonlinear functions via functional decomposition. The key contributions focus on intelligent placement of breakpoints for PWA approximations without requiring optimization, and on bounding the error of PWA compositions as a function of the error tolerance for each component of that composition. The proposed methods are used to systematically construct a PWA approximation for a complicated function, either to within a desired error tolerance or to a given level of complexity.

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arXiv2024

Reachability Analysis Using Hybrid Zonotopes and Functional Decomposition

This paper proposes methods for reachability analysis of nonlinear systems in both open loop and closed loop with advanced controllers. The methods combine hybrid zonotopes, a construct called a state-update set, functional decomposition, and special ordered set approximations to enable linear growth in reachable set memory complexity with time and linear scaling in computational complexity with the system dimension. Facilitating this combination are new identities for constructing nonconvex sets that contain nonlinear functions and for efficiently converting a collection of polytopes from vertex representation to hybrid zonotope representation. Benchmark numerical examples from the literature demonstrate the proposed methods and provide comparison to state-of-the-art techniques.

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arXiv2023

Set-valued State Estimation for Nonlinear Systems Using Hybrid Zonotopes

This paper proposes a method for set-valued state estimation of nonlinear, discrete-time systems. This is achieved by combining graphs of functions representing system dynamics and measurements with the hybrid zonotope set representation that can efficiently represent nonconvex and disjoint sets. Tight over-approximations of complex nonlinear functions are efficiently produced by leveraging special ordered sets and neural networks, which enable computation of set-valued state estimates that grow linearly in memory complexity with time. A numerical example demonstrates significant reduction of conservatism in the set-valued state estimates using the proposed method as compared to an idealized convex approach.

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