arXiv subjects

Amr Alanwar

Publications and source records attributed to Amr Alanwar.

At least 37 records · Page 2Linked to original sources

arXiv2026

Certifying Plans under Model Mismatch: A Trilemma for Reachability from Scarce Data

Sim-to-real policies are designed under nominal dynamics, but target-system trials may yield only a few isolated one-step transitions. We study pre-execution certification of a fixed control sequence, such as an action chunk produced by a learned policy. If the sequence reaches an unobserved state-input region, the observations remain consistent with target systems whose trajectories separate along it by an arbitrarily large amount. Any deterministic certifier sound for all of them must then decline to certify or return a reachable tube with arbitrarily large projected width. For bounded smooth classes of the target-nominal model error, we derive a finite plan-dependent projected-width lower bound. These results expose a trilemma among uniform trajectory containment, finite projected width, and unrestricted model-error behavior beyond the observations. ForeReach requires a supplied componentwise Lipschitz bound on the model error. Observed transition pairs can refute this declaration but cannot establish it outside the observed locations. Conditional on a valid declaration, our method constructs a set-membership envelope for the model error, propagates a zonotopic reachable tube, and certifies only when propagation remains within the certification domain and every projected tube slice avoids the unsafe set. In two benchmark systems, calibration baselines may remain narrow after losing trajectory containment outside data support, whereas our method declines to certify unsupported sequences and recovers certification when relevant target data and sufficient obstacle clearance are available.

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arXiv2026

Probabilistic Reachable-Action Verification of Visuomotor Policies via Set-Based Training

Reachability analysis for visuomotor policies is difficult because large visual encoders make end-to-end set propagation computationally expensive and excessively conservative. We therefore freeze the visual encoder and confine set propagation to a low-dimensional interface between it and the downstream policy, with the interface set calibrated from held-out camera-pose perturbations. Propagating this set through the policy with zonotopes yields a terminal output-enclosure width that set-based training optimizes directly. During evaluation, camera-pose perturbations are sampled from the prescribed distribution, and rollout-level split conformal calibration converts the resulting action-deviation scores into a probabilistic reachable-action radius with finite-sample coverage. In controlled manipulation experiments, set-based training reduces this radius while preserving closed-loop task capability, and matched behavior-only, observational-consistency, and pointwise-adversarial controls all leave a larger radius.

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arXiv2026

Secure Set-based State Estimation for Safety-Critical Applications under Adversarial Attacks on Sensors

Set-based state estimation provides guaranteed state inclusion certificates that are crucial for the safety verification of dynamical systems. However, when system sensors are subject to cyberattacks, maintaining both safety and security guarantees becomes a fundamental challenge. Existing point-based secure state estimation methods cannot adequately address this challenge because they cannot provide state inclusion certificates. This paper introduces a novel approach that simultaneously ensures safety guarantees through guaranteed state inclusion and security guarantees against sensor attacks, without imposing conservative restrictions on system operation. We propose a Secure Set-based State Estimation (S3E) algorithm that maintains the true system state within the estimated set under sensor attacks, provided the initialization set contains the initial state and the system remains observable from the uncompromised sensor subset. The algorithm provides the estimated set as a collection of constrained zonotopes (agreement sets), which can be used as robust certificates to verify whether the system adheres to safety constraints. Furthermore, we demonstrate that the estimated set remains unaffected by attack signals of sufficiently large magnitude and also establish sufficient conditions for attack detection, identification, and filtering. This compels the attacker to inject only signals of small magnitudes to evade detection, thus preserving the accuracy of the estimated set. To address the computational complexity of the algorithm, we offer several strategies for complexity-performance tradeoffs. The efficacy of the proposed algorithm is illustrated through several examples, including its application to a three-story building model.

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arXiv2026

GNN-DIP: Neural Corridor Selection for Decomposition-Based Motion Planning

Motion planning through narrow passages remains a core challenge: sampling-based planners rarely place samples inside these narrow but critical regions, and even when samples land inside a passage, the straight-line connections between them run close to obstacle boundaries and are frequently rejected by collision checking. Decomposition-based planners resolve both issues by partitioning free space into convex cells -- every passage is captured exactly as a cell boundary, and any path within a cell is collision-free by construction. However, the number of candidate corridors through the cell graph grows combinatorially with environment complexity, creating a bottleneck in corridor selection. We present GNN-DIP, a framework that addresses this by integrating a Graph Neural Network (GNN) with a two-phase Decomposition-Informed Planner (DIP). The GNN predicts portal scores on the cell adjacency graph to bias corridor search toward near-optimal regions while preserving completeness. In 2D, Constrained Delaunay Triangulation (CDT) with the Funnel algorithm yields exact shortest paths within corridors; in 3D, Slab convex decomposition with portal-face sampling provides near-optimal path evaluation. Benchmarks on 2D narrow-passage scenarios, 3D bottleneck environments with up to 246 obstacles, and dynamic 2D settings show that GNN-DIP achieves 99--100% success rates with 2--280 times speedup over sampling-based baselines.

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arXiv2026

Reachability Analysis With Probabilistic Zonotopes: Learning Realized Disturbances and Refining Aleatory Uncertainty

This paper develops a data-driven reachability framework for linear systems whose disturbances are modeled by probabilistic zonotopes (PZs), combining bounded deterministic and Gaussian stochastic components. In contrast to methods that require a precisely known disturbance model (either purely deterministic or purely stochastic), we assume only a conservative prior PZ and refine it from data. The framework separates two uncertainty sources: realized disturbances, which act along the collected trajectory and govern the size of the data-consistent model set, and aleatory disturbances, which enter as future additive uncertainty during reachable-set propagation; both shape the reachable sets, but through different mechanisms. Refinement exploits prior system knowledge together with trajectory-consistency constraints induced by the data, which impose affine couplings between deterministic and Gaussian latent variables. We accordingly develop a constrained-PZ calculus that absorbs the stochastic part of these constraints into an equivalent representation, removes infeasible latent directions, and reduces stochastic covariance, together with identification-aware fusion rules for combining heterogeneous constrained-PZ descriptions. The refined realized-disturbance proxies then serve as scenarios in a linear program that learns the smallest translated and scaled copy of the prior disturbance set that contains all proxy confidence sets while remaining nested in the prior. The resulting deterministic, high-probability reachable sets carry formal containment guarantees with substantially reduced conservatism, and numerical examples confirm that the pipeline tightens both the data-consistent model set and the propagated reachable sets.

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arXiv2026

Orthogonal Transformations for Efficient Data-Driven Reachability Analysis

Data-driven reachability analysis using matrix zonotopes faces a fundamental challenge: the number of generators in the reachable set grows exponentially during propagation, while current order reduction yields overly conservative approximations in data-driven settings. This paper introduces an orthogonal matrix-based framework that appropriately transfers the coordinate system before reducing the generators of the reachable set, dramatically reducing reachable set volumes. By exploiting the factorized structure of data-driven matrix zonotope generators, we develop several efficient algorithms to solve the problem. Numerical experiments demonstrate order-of-magnitude volume reductions compared to traditional methods, while maintaining comparable generator numbers. Our method provides a practical solution to improve precision in data-driven safety verification.

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arXiv2026

Data-Driven Reachability Analysis Using Matrix Perturbation Theory

We propose a matrix zonotope perturbation framework that leverages matrix perturbation theory to characterize how noise-induced distortions alter the dynamics within sets of models. The framework derives interpretable Cai-Zhang bounds for matrix zonotopes (MZs) and extends them to constrained matrix zonotopes (CMZs). Motivated by this analysis and the computational burden of CMZ-based reachable-set propagation, we introduce a coefficient-space approximation in which the constrained coefficient space of the CMZ is over-approximated by an unconstrained zonotope. Replacing CMZ-constrained-zonotope (CZ) products with unconstrained MZ-zonotope multiplication yields a simpler and more scalable reachable-set update. Experimental results demonstrate that the proposed method is substantially faster than the standard CMZ approach while producing reachable sets that are less conservative than those obtained with existing MZ-based methods, advancing practical, accurate, and real-time data-driven reachability analysis.

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arXiv2026

Informed Hybrid Zonotope-based Motion Planning Algorithm

Optimal path planning in nonconvex free spaces poses substantial computational challenges. A common approach formulates such problems as mixed-integer linear programs (MILPs); however, solving general MILPs is computationally intractable and severely limits scalability. To address these limitations, we propose HZ-MP, an informed Hybrid Zonotope-based Motion Planner, which decomposes the obstacle-free space and performs low-dimensional face sampling guided by an ellipsotope heuristic, thereby concentrating exploration on promising transition regions. This structured exploration mitigates the excessive wasted sampling that degrades existing informed planners in narrow-passage or enclosed-goal scenarios. We prove that HZ-MP is probabilistically complete and asymptotically optimal, and demonstrate empirically that it converges to high-quality trajectories within a small number of iterations.

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arXiv2026

From Points to Sets: Set-Based Safety Verification in the Latent Space

We extend latent representation methods for safety control design to set-valued states. Recent work has shown that barrier functions designed in a learned latent space can transfer safety guarantees back to the original system, but these methods evaluate certificates at single state points, ignoring state uncertainty. A fixed safety margin can partially address this but cannot adapt to the anisotropic and time-varying nature of the uncertainty gap across different safety constraints. We instead represent the system state as a zonotope, propagate it through the encoder to obtain a latent zonotope, and evaluate certificates over the worst case of the entire set. On a 16-dimensional quadrotor suspended-load gate passage task, set-valued evaluation achieves 5/5 collision-free passages, compared to 1/5 for point-based evaluation and 2/5 for a fixed-margin baseline. Set evaluation reports safety in 44.4% of per-head evaluations versus 48.5% for point-based, and this greater conservatism detects 4.1% blind spots where point evaluation falsely certifies safety, enabling earlier corrective control. The safety gap between point and set evaluation varies up to $12\times$ across certificate heads, explaining why no single fixed margin suffices and confirming the need for per-head, per-timestep adaptation, which set evaluation provides by construction.

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arXiv2026

Data-Driven Reachability Analysis with Optimal Input Design

This paper addresses the conservatism in data-driven reachability analysis for discrete-time linear systems subject to bounded process noise, where the system matrices are unknown and only input--state trajectory data are available. Building on the constrained matrix zonotope (CMZ) framework, two complementary strategies are proposed to reduce conservatism in reachable-set over-approximations. First, the standard Moore--Penrose pseudoinverse is replaced with a row-norm-minimizing right inverse computed via a second-order cone program (SOCP), which directly reduces the size of the resulting model set, yielding tighter generators and less conservative reachable sets. Second, an online A-optimal input design strategy is introduced to improve the informativeness of the collected data and the conditioning of the resulting model set, thereby reducing uncertainty. The proposed framework extends naturally to piecewise affine systems through mode-dependent data partitioning. Numerical results on a five-dimensional stable LTI system and a two-dimensional piecewise affine system demonstrate that combining designed inputs with the row-norm right inverse significantly reduces conservatism compared to a baseline using random inputs and the pseudoinverse, leading to tighter reachable sets for safety verification.

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arXiv2026

Bridging Data-Driven Reachability Analysis and Statistical Estimation via Constrained Matrix Convex Generators

Data-driven reachability analysis enables safety verification when first-principles models are unavailable. This requires constructing sets of system models consistent with measured trajectories and noise assumptions. Existing approaches rely on zonotopic or box-based approximations, which do not fit the geometry of common noise distributions such as Gaussian disturbances and can lead to significant conservatism, especially in high-dimensional settings. This paper builds on ellipsotope-based representations to introduce mixed-norm uncertainty sets for data-driven reachability. The highest-density region defines the exact minimum-volume noise confidence set, while Constrained Convex Generators (CCG) and their matrix counterpart (CMCG) provide compatible geometric representations at the noise and parameter level. We show that the resulting CMCG coincides with the maximum-likelihood confidence ellipsoid for Gaussian disturbances, while remaining strictly tighter than constrained matrix zonotopes for mixed bounded-Gaussian noise. For non-convex noise distributions such as Gaussian mixtures, a minimum-volume enclosing ellipsoid provides a tractable convex surrogate. We further prove containment of the CMCG times CCG product and bound the conservatism of the Gaussian-Gaussian interaction. Numerical examples demonstrate substantially tighter reachable sets compared to box-based approximations of Gaussian disturbances. These results enable less conservative safety verification and improve the accuracy of uncertainty-aware control design.

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arXiv2026

Data-Driven Nonconvex Reachability Analysis using Exact Set Propagation

This paper studies deterministic data-driven reachability analysis for dynamical systems with unknown dynamics and nonconvex reachable sets. Existing deterministic data-driven approaches typically employ zonotopic set representations, for which the multiplication between a zonotopic model set and a zonotopic state set cannot be represented algebraically exactly, thereby necessitating over-approximation steps in reachable-set propagation. To remove this structural source of conservatism, we introduce constrained polynomial matrix zonotopes (CPMZs) to represent data-consistent model sets, and show that the multiplication between a CPMZ model set and a constrained polynomial zonotope (CPZ) state set admits an algebraically exact CPZ representation. This property enables set propagation entirely within the CPZ representation, thereby avoiding propagation-induced over-approximation and even retaining the ability to represent nonconvex reachable sets. Moreover, we develop set-theoretic results that enable the intersection of data-consistent model sets as new data become available, yielding the proposed online refinement scheme that progressively tightens the data-consistent model set and, in turn, the resulting reachable set. Beyond linear systems, we extend the proposed framework to polynomial dynamics and develop additional set-theoretic results that enable both model-based and data-driven reachability analysis within the same algebraic representation. By deriving algebraically exact CPZ representations for monomials and their compositions, reachable-set propagation can be carried out directly at the set level without resorting to interval arithmetic or relaxation-based bounding techniques. Numerical examples for both linear and polynomial systems demonstrate a significant reduction in conservatism compared to state-of-the-art deterministic data-driven reachability methods.

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arXiv2026

Transformer-Accelerated Interpolated Data-Driven Reachability Analysis from Noisy Data

Data-driven reachability analysis provides guaranteed outer approximations of reachable sets from input-state measurements, yet each propagation step requires a matrix-zonotope multiplication whose cost grows with the horizon length, limiting scalability. We observe that data-driven propagation is inherently step-size sensitive, in the sense that set-valued operators at different discretization resolutions yield non-equivalent reachable sets at the same physical time, a property absent in model-based propagation. Exploiting this multi-resolution structure, we propose Interpolated Reachability Analysis (IRA), which computes a sparse chain of coarse anchor sets sequentially and reconstructs fine-resolution intermediate sets in parallel across coarse intervals. We derive a fully data-driven coarse-noise over-approximation that removes the need for continuous-time system knowledge, prove deterministic outer-approximation guarantees for all interpolated sets, and establish conditional tightness relative to the fine-resolution chain. To replace the remaining matrix-zonotope multiplications in the fine phase, we further develop Transformer-Accelerated IRA (TA-IRA), where an encoder-decoder Transformer is calibrated via split conformal prediction to provide finite-sample pointwise and path-wise coverage certificates. Numerical experiments on a five-dimensional linear system confirm the theoretical guarantees and demonstrate significant computational savings.

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arXiv2026

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

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.

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arXiv2026

Transformer-Enhanced Data-Driven Output Reachability with Conformal Coverage Guarantees

This paper considers output reachability analysis for linear time-invariant systems with unknown state-space matrices and unknown observation map, given only noisy input-output measurements. The Cayley--Hamilton theorem is applied to eliminate the latent state algebraically, producing an autoregressive input-output model whose parameter uncertainty is enclosed in a matrix zonotope. Set-valued propagation of this model yields output reachable sets with deterministic containment guarantees under a bounded aggregated residual assumption. The conservatism inherent in the lifted matrix-zonotope product is then mitigated by a decoder-only Transformer trained on labels obtained through directional contraction of the formal envelope via an exterior non-reachability certificate. Split conformal prediction restores distribution-free coverage at both per-step and trajectory levels without access to the true reachable-set hull. The framework is validated on a five-dimensional system with multiple unknown observation matrices.

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arXiv2026

Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees

We present a data-driven framework for reachability analysis of nonlinear dynamical systems that requires no explicit model. A denoising diffusion probabilistic model learns the time-evolving state distribution of a dynamical system from trajectory data alone. The predicted reachable set takes the form of a sublevel set of a nonconformity score derived from the reconstruction error, with the threshold calibrated via the Learn Then Test procedure so that the probability of excluding a reachable state is bounded with high probability. Experiments on three nonlinear systems, a forced Duffing oscillator, a planar quadrotor, and a high-dimensional reaction-diffusion system, confirm that the empirical miss rate remains below the Probably Approximately Correct (PAC) bound while scaling to state dimensions beyond the reach of classical grid-based and polynomial methods.

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arXiv2026

Certified Set Convergence for Piecewise Affine Systems via Neural Lyapunov Functions

Safety-critical control of piecewise affine (PWA) systems under bounded additive disturbances requires guarantees not for individual states but for entire state sets simultaneously: a single control action must steer every state in the set toward a target, even as sets crossing mode boundaries split and evolve under distinct affine dynamics. Certifying such set convergence via neural Lyapunov functions couples the Lipschitz constants of the value function and the policy, yet certified bounds for expressive networks exceed true values by orders of magnitude, creating a certification barrier. We resolve this through a three-stage pipeline that decouples verification from the policy. A value function from Hamilton-Jacobi backward reachability, trained via reinforcement learning, is the Lyapunov candidate. A permutation-invariant Deep Sets controller, distilled via regret minimization, produces a common action. Verification propagates zonotopes through the value network, yielding verified Lyapunov upper bounds over entire sets without bounding the policy Lipschitz constant. On four benchmarks up to dimension six, including systems with per-mode operator norms exceeding unity, the framework certifies set convergence with positive margin on every system. A spectrally constrained local certificate completes the terminal guarantee, and the set-actor is the only tested method to achieve full strict set containment, at constant-time online cost.

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arXiv2026

Inclusion conditions for the Constrained Polynomial Zonotopic case

Set operations are well understood for convex sets but become considerably more challenging in the non-convex case due to the loss of structural properties in their representation. Constrained polynomial zonotopes (CPZs) offer an effective compromise, as they can capture complex, typically non-convex geometries while maintaining an algebraic structure suitable for further manipulation. Building on this, we propose novel nonlinear encodings that provide sufficient conditions for testing inclusion between two CPZs and adapt them for seamless integration within optimization frameworks.

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