arXiv subjects

Florin Stoican

Publications and source records attributed to Florin Stoican.

At least 19 recordsLinked to original sources

arXiv2026

Zonotope-Based Elastic Tube Model Predictive Control

Tube-based Model Predictive Control (MPC) is a widely adopted robust control framework for constrained linear systems under additive disturbance. The paper is focused on reducing the numerical complexity associated with the tube parameterization, described as a sequence of elastically-scaled zonotopic sets. A new class of scaled-zonotope inclusion conditions is proposed, alleviating the need for a priori specification of certain set-containment constraints and achieving significant reductions in complexity. A comprehensive complexity analysis is provided for both the polyhedral and the zonotopic setting, illustrating the trade-off between an enlarged domain of attraction and the required computational effort. The proposed approach is validated through extensive numerical experiments.

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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

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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arXiv2026

On maximal positive invariant set computation for rank-deficient linear systems

The maximal positively invariant (MPI) set is obtained through a backward reachability procedure involving the iterative computation and intersection of predecessor sets under state and input constraints. However, standard static feedback synthesis may place some of the closed-loop eigenvalues at zero, leading to rank-deficient dynamics. This affects the MPI computation by inducing projections onto lower-dimensional subspaces during intermediate steps. By exploiting the Schur decomposition, we explicitly address this singular case and propose a robust algorithm that computes the MPI set in both polyhedral and constrained-zonotope representations.

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arXiv2026

Real-time loosely coupled GNSS and IMU integration via Factor Graph Optimization

Accurate positioning, navigation, and timing (PNT) is fundamental to the operation of modern technologies and a key enabler of autonomous systems. A very important component of PNT is the Global Navigation Satellite System (GNSS) which ensures outdoor positioning. Modern research directions have pushed the performance of GNSS localization to new heights by fusing GNSS measurements with other sensory information, mainly measurements from Inertial Measurement Units (IMU). In this paper, we propose a loosely coupled architecture to integrate GNSS and IMU measurements using a Factor Graph Optimization (FGO) framework. Because the FGO method can be computationally challenging and often used as a post-processing method, our focus is on assessing its localization accuracy and service availability while operating in real-time in challenging environments (urban canyons). Experimental results on the UrbanNav-HK-MediumUrban-1 dataset show that the proposed approach achieves real-time operation and increased service availability compared to batch FGO methods. While this improvement comes at the cost of reduced positioning accuracy, the paper provides a detailed analysis of the trade-offs between accuracy, availability, and computational efficiency that characterize real-time FGO-based GNSS/IMU fusion.

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arXiv2026

Real-time tightly coupled GNSS and IMU integration via Factor Graph Optimization

Reliable positioning in dense urban environments remains challenging due to frequent GNSS signal blockage, multipath, and rapidly varying satellite geometry. While factor graph optimization (FGO)-based GNSS-IMU fusion has demonstrated strong robustness and accuracy, most formulations remain offline. In this work, we present a real-time tightly coupled GNSS-IMU FGO method that enables causal state estimation via incremental optimization with fixed-lag marginalization, and we evaluate its performance in a highly urbanized GNSS-degraded environment using the UrbanNav dataset.

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arXiv2026

Safe Navigation in Cluttered Environments Via Spline-Based Harmonic Potential Fields

We provide a complete motion-planning mechanism that ensures target tracking and obstacle avoidance in a cluttered environment. For a given polyhedral decomposition of the feasible space, we adopt a novel procedure that constrains the agent to move only through a prescribed sequence of cells via a suitable control policy. For each cell, we construct a harmonic potential surface induced by a Dirichlet boundary condition given as a cardinal B-spline curve. A detailed analysis of the curve behavior (periodicity, support) and of the associated control point selection allows us to explicitly compute these harmonic potential surfaces, from which we subsequently derive the corresponding control policy. We illustrate that the resulting construction funnels the agent safely along the chain of cells from the starting point to the target.

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arXiv2025

Tight displacement-based formation control under bounded disturbances. A set-theoretic perspective

This paper investigates the synthesis of controllers for displacement-based formation control in the presence of bounded disturbances, specifically focusing on uncertainties originating from measurement noise. While the literature frequently addresses such problems using stochastic frameworks, this work proposes a deterministic methodology grounded in set-theoretic concepts. By leveraging the principles of set invariance, we adapt the theory of ultimate boundedness to the specific dynamics of displacement-based formations. This approach provides a rigorous method for analyzing the system's behavior under persistent disturbances. Furthermore, this set-theoretic framework allows for the optimized selection of the proposed control law parameters to guarantee pre-specified performance bounds. The efficacy of the synthesized controller is demonstrated in the challenging application of maintaining tight formations in a multi-obstacles environment.

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arXiv2025

Roundabout Constrained Convex Generators: A Unified Framework for Multiply-Connected Reachable Sets

This paper introduces Roundabout Constrained Convex Generators (RCGs), a set representation framework for modeling multiply connected regions in control and verification applications. The RCG representation extends the constrained convex generators framework by incorporating an inner exclusion zone, creating sets with topological holes that naturally arise in collision avoidance and safety-critical control problems. We present two equivalent formulations: a set difference representation that provides geometric intuition and a unified parametric representation that facilitates computational implementation. The paper establishes closure properties under fundamental operations, including linear transformations, Minkowski sums, and intersections with convex generator sets. We derive special cases, including roundabout zonotopes and roundabout ellipsotopes, which offer computational advantages for specific norm selections. The framework maintains compatibility with existing optimization solvers while enabling the representation of non-convex feasible regions that were previously challenging to model efficiently.

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arXiv2025

Explicit MPC for the constrained zonotope case with low-rank matrix updates

Solving the explicit Model Predictive Control (MPC) problem requires enumerating all critical regions and their associated feedback laws, a task that scales exponentially with the system dimension and the prediction horizon, as well. When the problem's constraints are boxes or zonotopes, the feasible domain admits a compact constrained-zonotope representation. Building on this insight, we exploit the geometric properties of the equivalent constrained-zonotope reformulation to accelerate the computation of the explicit solution. Specifically, we formulate the multi-parametric problem in the lifted generator space and solve it using second-order optimality conditions, employ low-rank matrix updates to reduce computation time, and introduce an analytic enumeration of candidate active sets that yields the explicit solution in tree form.

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arXiv2025

A comparison between joint and dual UKF implementations for state estimation and leak localization in water distribution networks

The sustainability of modern cities highly depends on efficient water distribution management, including effective pressure control and leak detection and localization. Accurate information about the network hydraulic state is therefore essential. This article presents a comparison between two data-driven state estimation methods based on the Unscented Kalman Filter (UKF), fusing pressure, demand and flow data for head and flow estimation. One approach uses a joint state vector with a single estimator, while the other uses a dual-estimator scheme. We analyse their main characteristics, discussing differences, advantages and limitations, and compare them theoretically in terms of accuracy and complexity. Finally, we show several estimation results for the L-TOWN benchmark, allowing to discuss their properties in a real implementation.

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arXiv2025

An ANN-Enhanced Approach for Flatness-Based Constrained Control of Nonlinear Systems

Neural networks have proven practical for a synergistic combination of advanced control techniques. This work analyzes the implementation of rectified linear unit neural networks to achieve constrained control in differentially flat systems. Specifically, the class of flat systems enjoys the benefit of feedback linearizability, i.e., the systems can be linearized by means of a proper variable transformation. However, the price for linearizing the dynamics is that the constraint descriptions are distorted geometrically. Our results show that, by using neural networks, these constraints can be represented as a union of polytopes, enabling the use of mixed-integer programming tools to guarantee constraint satisfaction. We further analyze the integration of the characterization into efficient settings such as control Lyapunov function-based and model predictive control (MPC). Interestingly, this description also allows us to explicitly compute the solution of the MPC problem for the nonlinear system. Several examples are provided to illustrate the effectiveness of our framework.

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arXiv2025

Factor Graph Optimization for Leak Localization in Water Distribution Networks

Detecting and localizing leaks in water distribution network systems is an important topic with direct environmental, economic, and social impact. Our paper is the first to explore the use of factor graph optimization techniques for leak localization in water distribution networks, enabling us to perform sensor fusion between pressure and demand sensor readings and to estimate the network's temporal and structural state evolution across all network nodes. The methodology introduces specific water network factors and proposes a new architecture composed of two factor graphs: a leak-free state estimation factor graph and a leak localization factor graph. When a new sensor reading is obtained, unlike Kalman and other interpolation-based methods, which estimate only the current network state, factor graphs update both current and past states. Results on Modena, L-TOWN and synthetic networks show that factor graphs are much faster than nonlinear Kalman-based alternatives such as the UKF, while also providing improvements in localization compared to state-of-the-art estimation-localization approaches. Implementation and benchmarks are available at https://github.com/pirofti/FGLL.

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arXiv2024

Dual Unscented Kalman Filter Architecture for Sensor Fusion in Water Networks Leak Localization

Leakage in water systems results in significant daily water losses, degrading service quality, increasing costs, and aggravating environmental problems. Most leak localization methods rely solely on pressure data, missing valuable information from other sensor types. This article proposes a hydraulic state estimation methodology based on a dual Unscented Kalman Filter (UKF) approach, which enhances the estimation of both nodal hydraulic heads, critical in localization tasks, and pipe flows, useful for operational purposes. The approach enables the fusion of different sensor types, such as pressure, flow and demand meters. The strategy is evaluated in well-known open source case studies, namely Modena and L-TOWN, showing improvements over other state-of-the-art estimation approaches in terms of interpolation accuracy, as well as more precise leak localization performance in L-TOWN.

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arXiv2023

Nodal Hydraulic Head Estimation through Unscented Kalman Filter for Data-driven Leak Localization in Water Networks

In this paper, we present a nodal hydraulic head estimation methodology for water distribution networks (WDN) based on an Unscented Kalman Filter (UKF) scheme with application to leak localization. The UKF refines an initial estimation of the hydraulic state by considering the prediction model, as well as available pressure and demand measurements. To this end, it provides customized prediction and data assimilation steps. Additionally, the method is enhanced by dynamically updating the prediction function weight matrices. Performance testing on the Modena benchmark under realistic conditions demonstrates the method's effectiveness in enhancing state estimation and data-driven leak localization.

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arXiv2023

Learning Dictionaries from Physical-Based Interpolation for Water Network Leak Localization

This article presents a leak localization methodology based on state estimation and learning. The first is handled by an interpolation scheme, whereas dictionary learning is considered for the second stage. The novel proposed interpolation technique exploits the physics of the interconnections between hydraulic heads of neighboring nodes in water distribution networks. Additionally, residuals are directly interpolated instead of hydraulic head values. The results of applying the proposed method to a well-known case study (Modena) demonstrated the improvements of the new interpolation method with respect to a state-of-the-art approach, both in terms of interpolation error (considering state and residual estimation) and posterior localization.

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arXiv2021

Data-driven Leak Localization in Water Distribution Networks via Dictionary Learning and Graph-based Interpolation

In this paper, we propose a data-driven leak localization method for water distribution networks (WDNs) which combines two complementary approaches: graph-based interpolation and dictionary classification. The former estimates the complete WDN hydraulic state (i.e., hydraulic heads) from real measurements at certain nodes and the network graph. Then, these actual measurements, together with a subset of valuable estimated states, are used to feed and train the dictionary learning scheme. Thus, the meshing of these two methods is explored, showing that its performance is superior to either approach alone, even deriving different mechanisms to increase its resilience to classical problems (e.g., dimensionality, interpolation errors, etc.). The approach is validated using the L-TOWN benchmark proposed at BattLeDIM2020.

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arXiv2020

Fault Handling in Large Water Networks with Online Dictionary Learning

Fault detection and isolation in water distribution networks is an active topic due to its model's mathematical complexity and increased data availability through sensor placement. Here we simplify the model by offering a data driven alternative that takes the network topology into account when performing sensor placement and then proceeds to build a network model through online dictionary learning based on the incoming sensor data. Online learning is fast and allows tackling large networks as it processes small batches of signals at a time and has the benefit of continuous integration of new data into the existing network model, be it in the beginning for training or in production when new data samples are encountered. The algorithms show good performance when tested on both small and large-scale networks.

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