arXiv subjects

Rafael Vazquez

Publications and source records attributed to Rafael Vazquez.

At least 19 recordsLinked to original sources

arXiv2026

A heteroskedasticity and autocorrelation consistent test for process noise calibration of Kalman filters in multi-sensor orbit determination

Process noise calibration is a central problem in sequential orbit determination. If the process noise covariance is too small the filter is overconfident, and if it is too large it is overconservative. In both cases the estimation error grows and the reported covariance stops describing it, which affects downstream products such as conjunction assessment or re-entry prediction. No widely adopted method diagnoses the calibration in multi-sensor settings, where measurements of different type and dimension must enter a single consistency metric. This work presents the Heteroskedasticity and Autocorrelation Consistent Dimensionless Averaged Normalised Innovation Squared (HAC-DANIS) test, which evaluates process noise calibration from the innovation sequence of the filter, without ground truth. The normalised innovation squared (NIS) of each measurement is divided by its dimension, which puts sensors of any dimension on a common scale, and the standard error of the averaged sequence is obtained with the heteroskedasticity and autocorrelation consistent (HAC) Newey--West estimator, which accounts for the sensor-dependent variance of the sequence and for the serial correlation left by a miscalibrated filter or an imperfect dynamical model. Under mixing and moment conditions the statistic is asymptotically standard normal for a calibrated filter, and for a miscalibrated one its sign indicates the direction of the miscalibration. The autocorrelation function of the normalised sequence complements the test with a characterisation of the mistuning regime. Applied to an unscented Kalman filter processing simulated laser, telescope and radar observations of four satellites in low Earth orbit, the test rejects the eight miscalibrated process noise configurations with the sign of their miscalibration and does not reject the four calibrated with it.

physics.space-ph↗

arXiv2026

Explicit Globally Asymptotically Stable Attitude Control with Reaction Wheel Angular Momentum and Torque Constraints

We present an explicit Lyapunov attitude controller for rigid spacecraft actuated by three orthogonally mounted reaction wheels, parameterized using Modified Rodrigues Parameters (MRPs), which enforces hard bounds on wheel angular momentum and applied torque at every instant without solving any online optimization. A barrier-inspired momentum feedback prevents wheel saturation; a continuous positive scalar uniformly scales the feedback whenever a torque limit would otherwise be breached, preserving Lyapunov convergence. For the regulation problem, global asymptotic stability (GAS) is established via LaSalle's invariance principle, and constraint satisfaction is proved analytically for arbitrary symmetric positive-definite inertia matrices. Replacing the barrier by an error-state counterpart extends the design to tracking, with asymptotic (though no longer global) stability and the same safety guarantees under explicit feasibility conditions on the reference. Simulations confirm convergence and constraint satisfaction, and compare performance against other controllers.

math.OC↗

arXiv2026

Adaptively-refinable polar-spline discrete differential forms: hierarchical construction, exactness, and applications

A common approach to representing disk-like and sphere-like geometries in isogeometric analysis is to use collapsed-edge singularities in the underlying parameterization. The resulting tensor-product B-spline spaces on such singular parameterizations lack the required smoothness to be used in isogeometric analysis. Polar splines (Toshniwal et al., CMAME 2017) rectify this issue by extracting a smoother subspace, and have been successfully used to discretize high-order partial differential equations, as well as to perform structure-preserving discretizations of the de Rham complex.The latter is particularly relevant for mixed formulations that appear in applications such as electromagnetism and fluid dynamics. The main contributions of this paper are twofold. We combine the polar spline construction with hierarchical splines to obtain adaptively-refinable polar splines. Moreover, we do so in the context of structure-preserving methods. That is, we show how to construct hierarchical polar spline $k$-form spaces, prove that the corresponding basis functions are linearly independent, and prove that they form a cohomologically-correct discrete de Rham complex. These contributions provide a mathematically sound foundation for adaptive structure-preserving simulations on polar geometries. We also provide numerical experiments that validate the theory and illustrate the practical behavior of the construction with problems where preserving the structure is mandatory. These include a study of spurious harmonics that highlights how cohomology-breaking refinements differ between the polar and tensor-product settings, a discretization of a Maxwell eigenvalue problem on a locally-refined polar mesh, and an adaptive convergence study for a Hodge--Laplace problem.

math.NA↗

arXiv2026

LQR Design For Formation Flying Near Halo Orbits Exploiting Quasi-Periodic Symmetry In Toroidal Coordinates

This work presents the design of a Linear Quadratic Regulator for relative motion control near periodic orbits in the Circular Restricted Three-Body Problem (CR3BP), formulated in non-singular toroidal coordinates. The key result exploits the rotational quasi-periodicity of the toroidal coordinate transformation. A uniqueness argument on the stabilizing solution of the associated difference Riccati equation proves the optimal control gains need only be computed for a single orbital period. The controller is validated against the full non-linear CR3BP dynamics on an L1 Northern halo orbit in the Earth-Moon system, and further against a high-fidelity ephemeris model, demonstrating successful reconfiguration maneuvers on the invariant torus with low control effort. Compared with an impulsive targeting and station-keeping baseline, the proposed controller attains a comparable tracking accuracy while reducing the total control effort by approximately 40%.

physics.space-ph↗

arXiv2026

Output-Feedback Boundary Control of Reaction--Diffusion PDEs on Arbitrary Lipschitz Domains: A Target-Domain Approach

We present a domain-extension framework for output-feedback boundary stabilization of reaction-diffusion equations on arbitrary bounded Lipschitz domains, including non-convex and multiply connected geometries. The plant is posed on an irregular domain whose boundary has actuated and uncontrolled portions. Just as backstepping transforms the plant dynamics into a stable target system, the method embeds the plant in a target domain, such as a ball or a rectangle, where a stabilizing design is already known. Every boundary portion through which the extension proceeds must carry actuation and the complementary collocated measurement. Uncontrolled portions are allowed when they are shared with the target boundary and have the same boundary-condition type. The gap between the two domains is filled with a virtual copy of the plant dynamics, coupled to the plant through interface conditions, and the concatenated state evolves exactly as the known closed loop on the target domain. Well-posedness and exponential stability of the physical state follow by restriction. The offline design data are inherited from the target design and are closed-form for constant-coefficient plants on balls and rectangles. Online simulation of the virtual PDE has the same computational character as a full-order PDE observer, a standard component of output-feedback designs. A new explicit Neumann-actuated backstepping law on n-balls enlarges the available target designs. Output feedback is obtained by lifting the target-domain observer, driven by a collocated interface measurement relayed through the virtual domain. Numerical experiments on star-shaped, horseshoe, and multiply connected domains, with a partitioned plant/controller implementation and a shared-wall cavity, test the designs.

math.OC↗

arXiv2026

EOS-Bench: A Comprehensive Benchmark for Earth Observation Satellite Scheduling

Earth observation satellite imaging scheduling is a challenging NP-hard combinatorial optimisation problem central to space mission operations. While next-generation agile Earth observation satellites (EOS) increase operational flexibility, they also significantly raise scheduling complexity. The lack of a unified, open-source benchmark makes it difficult to compare algorithms across studies. This paper introduces EOS-Bench, a comprehensive framework for systematic and reproducible evaluation of scheduling methods. By integrating high-fidelity orbital dynamics and platform constraints, EOS-Bench generates 1,390 scenarios and 13,900 benchmark instances, spanning from small-scale validation cases to large coordination problems with up to 1,000 satellites and 10,000 requests. We further propose a scenario characterisation scheme to quantify structural difficulty based on factors such as opportunity density, task flexibility, conflict intensity, and satellite congestion. A multidimensional evaluation protocol is introduced, assessing performance across five metrics: task profit, completion rate, workload balance, timeliness, and runtime. The framework is evaluated using mixed-integer programming, heuristics, meta-heuristics, and deep reinforcement learning across both agile and non-agile settings. Results show that EOS-Bench effectively distinguishes solver performance across scales and conditions, revealing trade-offs between solution quality and computational efficiency, and providing deeper insight into scenario complexity. EOS-Bench offers a unified and extensible open testbed for advancing research in Earth observation satellite scheduling. The code and data are available at https://github.com/Ethan19YQ/EOS-Bench.

cs.NI↗

arXiv2026

Closed-Form Solutions to the Fokker-Planck Equation for Orbital Uncertainty Propagation

Non-Gaussian tails dominate collision probability estimates in conjunction assessment, yet capturing them without Monte Carlo sampling is challenging, especially when process noise is included. We present a closed-form, grid-free solution to the Fokker-Planck equation by proving that an exponential-of-quadratic-form ansatz is structurally preserved under advection and diffusion. The probability density function propagates via a compact ODE system, significantly cheaper than Monte Carlo and without spatial discretization. As an application, the method performs orbit uncertainty propagation under stochastic forcing representative of atmospheric drag. Results demonstrate the method faithfully captures non-Gaussian features, asymmetric tails, and stochastic broadening, matching a Monte Carlo benchmark.

physics.space-ph↗

arXiv2025

A Switching Strategy for Event-Trigger Control of Spacecraft Rendezvous

This paper presents the design of a state-feedback control law for spacecraft rendezvous, formulated using the Hill-Clohessy-Wiltshire equations. The proposed method introduces an impulsive control strategy to regulate thruster operations. Specifically, a state-dependent switching framework is developed to determine both the control input magnitudes and the precise state conditions that trigger thruster activation. The nonlinear control law is derived using principles from automatic control theory, particularly Lyapunov stability analysis and the Linear Matrix Inequality framework. The resulting closed-loop system is proven to be stable, while simultaneously minimizing the total number of actuation events. The effectiveness of the proposed method is demonstrated through a numerical case study, which includes a comparative analysis with a standard Model Predictive Control scheme, highlighting the advantages and trade-offs of the developed control structure.

eess.SY↗

arXiv2025

Backstepping for Partial Differential Equations:A Survey

Systems modeled by partial differential equations (PDEs) are at least as ubiquitous as systems that are by nature finite-dimensional and modeled by ordinary differential equations (ODEs). And yet, systematic and readily usable methodologies, for such a significant portion of real systems, have been historically scarce. Around the year 2000, the backstepping approach to PDE control began to offer not only a less abstract alternative to PDE control techniques replicating optimal and spectrum assignment techniques of the 1960s, but also enabled the methodologies of adaptive and nonlinear control, matured in the 1980s and 1990s, to be extended from ODEs to PDEs, allowing feedback synthesis for physical and engineering systems that are uncertain, nonlinear, and infinite-dimensional. The PDE backstepping literature has grown in its nearly a quarter century of development to many hundreds of papers and nearly a dozen books. This survey aims to facilitate the entry, for a new researcher, into this thriving area of overwhelming size and topical diversity. Designs of controllers and observers, for parabolic, hyperbolic, and other classes of PDEs, in one and more dimensions (in box and spherical geometries), with nonlinear, adaptive, sampled-data, and event-triggered extensions, are covered in the survey. The lifeblood of control are technology and physics. The survey places a particular emphasis on applications that have motivated the development of the theory and which have benefited from the theory and designs: applications involving flows, flexible structures, materials, thermal and chemically reacting dynamics, energy (from oil drilling to batteries and magnetic confinement fusions), and vehicles.

math.OC↗

arXiv2025

Block Backstepping for Isotachic Hyperbolic PDEs and Multilayer Timoshenko Beams

In this paper, we investigate the rapid stabilization of N-layer Timoshenko composite beams with anti-damping and anti-stiffness at the uncontrolled boundaries. The problem of stabilization for a two-layer composite beam has been previously studied by transforming the model into a 1-D hyperbolic PIDE-ODE form and then applying backstepping to this new system. In principle this approach is generalizable to any number of layers. However, when some of the layers have the same physical properties (as e.g. in lamination of repeated layers), the approach leads to isotachic hyperbolic PDEs (i.e. where some states have the same transport speed). This particular yet physical and interesting case has not received much attention beyond a few remarks in the early hyperbolic design. Thus, this work starts by extending the theory of backstepping control of (m + n) hyperbolic PIDEs and m ODEs to blocks of isotachic states, leading to a block backstepping design. Then, returning to multilayer Timoshenko beams, the Riemann transformation is used to transform the states of N-layer Timoshenko beams into a 1-D hyperbolic PIDE-ODE system. The block backstepping method is then applied to this model, obtaining closed-loop stability of the origin in the L2 sense. An arbitrarily rapid convergence rate can be obtained by adjusting control parameters. Finally, numerical simulations are presented corroborating the theoretical developments.

math.OC↗

arXiv2025

Backstepping Control Laws for Higher-Dimensional PDEs: Spatial Invariance and Domain Extension Methods

This paper extends backstepping to higher-dimensional PDEs by leveraging domain symmetries and structural properties. We systematically address three increasingly complex scenarios. First, for rectangular domains, we characterize boundary stabilization with finite-dimensional actuation by combining backstepping with Fourier analysis, deriving explicit necessary conditions. Second, for reaction-diffusion equations on sector domains, we use angular eigenfunction expansions to obtain kernel solutions in terms of modified Bessel functions. Finally, we outline a domain extension method for irregular domains, transforming the boundary control problem into an equivalent one on a target domain. This framework unifies and extends previous backstepping results, offering new tools for higher-dimensional domains where classical separation of variables is inapplicable.

math.OC↗

arXiv2025

Orbit-Attitude Predictive Control in the Vicinity of Asteroids with In Situ Gravity Estimation

This paper presents an integrated model-learning predictive control scheme for spacecraft orbit-attitude station-keeping in the vicinity of asteroids. The orbiting probe relies on optical and laser navigation while attitude measurements are provided by star trackers and gyroscopes. The asteroid gravity field inhomogeneities are assumed to be unknown a priori. The state and gravity model parameters are estimated simultaneously using an unscented Kalman filter. The proposed gravity model identification enables the application of a learning-based predictive control methodology. The predictive control allows for a high degree of accuracy because the predicted model is progressively identified in situ. Consequently, the tracking errors decrease over time as the model accuracy increases. Finally, a constellation mission concept is analyzed in order to speed up the model identification process. Numerical results are shown and discussed.

eess.SY↗

arXiv2025

A flatness-based predictive controller for six-degrees of freedom spacecraft rendezvous

This work presents a closed-loop guidance algorithm for six-degrees of freedom spacecraft rendezvous with a passive target flying in an eccentric orbit. The main assumption is that the chaser vehicle has an attitude control system, based on reaction wheels, providing the necessary torque to change its orientation whereas the number of thrusters is arbitrary. The goal is to design fuel optimal maneuvers while satisfying operational constraints and rejecting disturbances. The proposed method is as follows; first, the coupled translational and angular dynamics are transformed to equivalent algebraic relations using the relative translational states transition matrix and the attitude flatness property. Then, a direct transcription method, based on B-splines parameterization and discretization of time continuous constraints, is developed to obtain a tractable static program. Finally, a Model Predictive Controller, based on linearization around the previously computed solution, is considered to handle disturbances. Numerical results are shown and discussed.

eess.SY↗

arXiv2025

Chance-constrained Model Predictive Control for Near Rectilinear Halo Orbit spacecraft rendezvous

This work presents a robust Model Predictive Controller (MPC) to solve the problem of spacecraft rendezvous in the context of the restricted three-body problem (R3BP) as will be required to dock with space stations in cislunar space. The employed methodology is both valid for chemical and electric thrusters. By exploiting the state transition matrix and using a chance-constrained approach, the robust MPC assures constraints satisfaction under the presence of disturbances in a probabilistic sense. The perturbations parameters are computed on-line using a disturbance estimator. The robust controller is tested for a rendezvous scenario with a target placed in an Earth-Moon Near-Rectilinear Halo Orbit. Numerical results are shown and discussed.

eess.SY↗

arXiv2025

Event-Based Impulsive Control for Spacecraft Rendezvous Hovering Phases

This work presents an event-triggered controller for spacecraft rendezvous hovering phases. The goal is to maintain the chaser within a bounded region with respect to the target. The main assumption is that the chaser vehicle has impulsive thrusters. These are assumed to be orientable at any direction and are constrained by dead-zone and saturation bounds. The event-based controller relies on trigger rules deciding when a suitable control law is applied. The local control law consists on a single impulse; therefore the trigger rules design is based on the instantaneous reachability to the admissible set. The final outcome is a very efficient algorithm from both computational burden and footprint perspectives. Because the proposed methodology is based on a single impulse control, the controller invariance is local and assessed through impulsive systems theory. Finally, numerical results are shown and discussed.

eess.SY↗

arXiv2024

A novel conjunction filter based on the minimum distance between perturbed trajectories

The increasing congestion in the near-Earth space environment has amplified the need for robust and efficient conjunction analysis techniques including the computation of the minimum distance between orbital paths in the presence of perturbations. After showing that classical Minimum Orbit Intersection Distance (MOID) computation schemes are unsuitable to treat Earth orbiting objects, the article presents an analytical approach to provide a more accurate estimate of the true distance between perturbed trajectories by incorporating the effect of zonal harmonics of arbitrary order. Cook's linear secular theory for the motion of the eccentricity vector is extended to include higher order eccentricity effects and applied to the computation of the minimum and maximum radii attained by two orbits at their mutual nodes, which can be employed to estimate the true distance between the two orbital paths and to establish an efficient algorithm for determining or excluding potential conjunctions. Extensive testing and validation are conducted using a high-fidelity propagator and a comprehensive dataset of resident space objects. The results demonstrate an accuracy below the km level for the orbit distance computation in 99\% of cases, which enables high-efficiency conjunction filtering.

astro-ph.EP↗

arXiv2024

Gain-Only Neural Operators for PDE Backstepping

In this work we advance the recently-introduced deep learning-powered approach to PDE backstepping control by proposing a method that approximates only the control gain function -- a function of one variable -- instead of the entire kernel function of the backstepping transformation, which depends on two variables. This idea is introduced using several benchmark unstable PDEs, including hyperbolic and parabolic types, and extended to 2X2 hyperbolic systems. By employing a backstepping transformation that utilizes the exact kernel (suitable for gain scheduling) rather than an approximated one (suitable for adaptive control), we alter the quantification of the approximation error. This leads to a significant simplification in the target system, shifting the perturbation due to approximation from the domain to the boundary condition. Despite the notable differences in the Lyapunov analysis, we are able to retain stability guarantees with this simplified approximation approach. Approximating only the control gain function simplifies the operator being approximated and the training of its neural approximation, potentially reducing the neural network size. The trade-off for these simplifications is a more intricate Lyapunov analysis, involving higher Sobolev spaces for some PDEs, and certain restrictions on initial conditions arising from these spaces. It is crucial to carefully consider the specific requirements and constraints of each problem to determine the most suitable approach; indeed, recent works have demonstrated successful applications of both full-kernel and gain-only approaches in adaptive control and gain scheduling contexts.

eess.SY↗

arXiv2024

Short-Term Space Occupancy and Conjunction Filter

Conjunction analysis (CA) for resident space objects (RSOs) is essential for preventing collisions in an increasingly crowded orbital environment and preserving the operational integrity of satellites. A first and fundamental step in the CA process is to estimate the range of altitudes that each object can occupy, throughout an operational screening time of, typically, a few days. In this paper, a method is poroposed to analytically evaluate such range of altitudes in a zonal problem model and for a time horizon of generic duration thereby generalizing the concept of space occupancy (SO) introduced in a recent work. The proposed method is exploited to construct a new conjunction filter that considerably improves the classical apogee-perigee filter routinely employed in CA. The effectiveness of the new filter is assessed in a low-Earth orbit (LEO) scenario using a high-fidelity perturbation model across a broad spectrum of orbits and conjunction geometries. Additionally, the method is applied to space traffic management providing a rapid and efficient means to examine the radial overlap of RSOs in LEO and track its progression in time.

physics.space-ph↗