arXiv subjects

Daniel Alazard

Publications and source records attributed to Daniel Alazard.

At least 19 recordsLinked to original sources

arXiv2025

Robust H2/H-infinity control under stochastic requirements: minimizing conditional value-at-risk instead of worst-case performance

Conventional robust H2/H-infinity control minimizes the worst-case performance, often leading to a conservative design driven by very rare parametric configurations. To reduce this conservatism while taking advantage of the stochastic properties of Monte Carlo sampling and its compatibility with parallel computing, we introduce an alternative paradigm that optimizes the controller with respect to a stochastic criterion, namely the conditional value at risk. We present the problem formulation and discuss several open challenges toward a general synthesis framework. The potential of this approach is illustrated on a mechanical system, where it significantly improves overall performance by tolerating some degradation in very rare worst-case scenarios.

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arXiv2025

Worst-case search in constrained uncertainty space for robust H-infinity synthesis

Standard linear H-infinity/H2 robust control and analysis tools operate on uncertain parameters assumed to vary independently within prescribed bounds. This paper extends their capabilities in the presence of nonlinear constraints coupling these parameters and restricting the parametric space. Based on the theory of upper-C1 functions, it is shown that the sequential quadratic programming (SQP) algorithm can be slightly adapted to address the search for worst-case H-infinity norm, a nonsmooth constrained optimization problem, and the search for worst-case stability under some assumptions. Specifically, we prove that for such upper-C1 functions, any subgradient provides a descent direction and satisfies Karush-Kuhn-Tucker (KKT) conditions at a local minimum, and that any accumulation point generated by SQP is a KKT point. This worst-case search then enables robust controller synthesis using a standard active configurations approach. Through an application to the robust control of a satellite, the proposed approach is shown to provide a scalable framework for robustness analysis and robust controller synthesis.

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arXiv2025

Non-linear dynamics of multibody systems: a system-based approach

This paper presents causal block-diagram models to represent the equations of motion of multi-body systems in a very compact and simple closed form. Both the forward dynamics (from the forces and torques imposed at the various degrees-of-freedom to the motions of these degrees-of-freedom) or the inverse dynamics (from the motions imposed at the degrees-of-freedom to the resulting forces and torques) can be considered and described by a block diagram model. This work extends the Two-Input Two-Output Port (TITOP) theory by including all non-linear terms and uniform or gravitational acceleration fields. Connection among different blocks is possible through the definition of the motion vector. The model of a system composed of a floating base, rigid bodies, revolute and prismatic joints, working under gravity is developed to illustrate the methodology. The proposed model is validated by simulation and cross-checking with a model built using an alternative modeling tool on a scenario where the nonlinear terms are determining.

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arXiv2024

Dynamics modelling and path optimization for the on-orbit assembly of large flexible structures using a multi-arm robot

This paper presents a comprehensive methodology for modeling an on-orbit assembly mission scenario of a large flexible structure using a multi-arm robot. This methodology accounts for significant changes in inertia and flexibility throughout the mission, addressing the problem of coupling dynamics between the robot and the evolving flexible structure during the assembly phase. A three-legged walking robot is responsible for building the structure, with its primary goal being to walk stably on the flexible structure while picking up, carrying and assembling substructure components. To accurately capture the dynamics and interactions of all subsystems in the assembly scenario, various linear fractional representations (LFR) are developed, considering the changing geometrical configuration of the multi-arm robot, the varying flexible dynamics and uncertainties. A path optimization algorithm is proposed for the multi-arm robot, capable of selecting trajectories based on various cost functions related to different performance and stability metrics. The obtained results demonstrate the effectiveness of the proposed modeling methodology and path optimization algorithm.

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arXiv2024

European Satellite Benchmark for Control Education and Industrial Training

To overcome the innovation gap of the Guidance, Navigation and Control (GNC) design process between research and industrial practice a benchmark of industrial relevance has been developed and is presented. This initiative is driven as well by the necessity to train future GNC engineers and the GNC space community on a set of identified complex problems. It allows to demonstrate the relevance of state-of-the-art modeling, control and analysis algorithms for future industrial adoption. The modeling philosophy for robust control synthesis, analysis including the control architecture that enables the simulation of the mission, i.e. the acquisition of a high pointing space mission, are provided.

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arXiv2024

Modeling and analysis of a flexible spinning Euler-Bernoulli beam with centrifugal stiffening and softening: A Linear Fractional Representation approach with application to spinning spacecraft

The derivation of a linear fractional representation (LFR) model for a flexible, spinning and uniform Euler-Bernoulli beam is accomplished using the {Lagrange} technique, fully capturing the centrifugal force generated by the spinning motion and accounting for its dependence on the angular velocity. This six degrees of freedom (DOF) model accounts for the behavior of deflection in the moving body frame, encompassing the bending, traction and torsion dynamics. The model is also designed to be compliant with the Two-Input-Two-Output Port (TITOP) approach, which offers the possibility to model complex multibody mechanical systems, while keeping the uncertain nature of the plant and condensing all the possible mechanical configurations in a single LFR. To evaluate the effectiveness of the model, various scenarios are considered and their results are tabulated. These scenarios include uniform beams with fixed root boundary conditions for different values of tip mass, root offset and angular velocity. The results from the analysis of the uniform cantilever beam are compared with solutions found in the literature and obtained from a commercial finite element software. Ultimately, this paper presents a multibody model for a spinning spacecraft mission scenario. A comprehensive analysis of the system dynamics is conducted, providing insights into the behavior of the spacecraft under spinning conditions.

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arXiv2023

Graph-Based Convexification of Nested Signal Temporal Logic Constraints for Trajectory Optimization

Optimizing high-level mission planning constraints is traditionally solved in exponential time and requires to split the problem into several ones, making the connections between them a convoluted task. This paper aims at generalizing recent works on the convexification of Signal Temporal Logic (STL) constraints converting them into linear approximations. Graphs are employed to build general linguistic semantics based on key words (such as Not, And, Or, Eventually, Always), and super-operators (e.g., Until, Implies, If and Only If) based on already defined ones. Numerical validations demonstrate the performance of the proposed approach on two practical use-cases of satellite optimal guidance using a modified Successive Convexification scheme.

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arXiv2023

Robust Optimization, Structure/Control co-design, Distributed Optimization, Monolithic Optimization, Robust Control, Parametric Uncertainty

This paper presents an end-to-end framework for robust structure/control optimization of an industrial benchmark. When dealing with space structures, a reduction of the spacecraft mass is paramount to minimize the mission cost and maximize the propellant availability. However, a lighter design comes with a bigger structural flexibility and the resulting impact on control performance. Two optimization architectures (distributed and monolithic) are proposed in order to face this issue. In particular the Linear Fractional Transformation (LFT) framework is exploited to formally set the two optimization problems by including parametric uncertainties. Large sets of uncertainties have to be indeed taken into account in spacecraft control design due to the impossibility to completely validate structural models in micro-gravity conditions with on-ground experiments and to the evolution of spacecraft dynamics during the mission (structure degradation and fuel consumption). In particular the Two-Input Two-Output Port (TITOP) multi-body approach is used to build the flexible dynamics in a minimal LFT form. The two proposed optimization algorithms are detailed and their performance are compared on an ESA future exploration mission, the ENVISION benchmark. With both approaches, an important reduction of the mass is obtained by coping with the mission's control performance/stability requirements and a large set of uncertainties.

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arXiv2023

Satellite Dynamics Toolbox Library: a tool to model multi-body space systems for robust control synthesis and analysis

The level of maturity reached by robust control theory techniques nowadays contributes to a considerable minimization of the development time of an end-to-end control design of a spacecraft system. The advantage offered by this framework is twofold: all system uncertainties can be included from the very beginning of the design process; the validation and verification (V\&V) process is improved by fast detection of worst-case configurations that could escape to a classical sample-based Monte Carlo simulation campaign. Before proceeding to the control synthesis and analysis, a proper uncertain plant model has to be available in order to push these techniques to their limits of performance. In this spirit, the Satellite Dynamics Toolbox Library (SDTlib) offers many features to model a spacecraft system in a multi-body fashion on SIMULINK. Parametric models can be easily built in a Linear Fractional Transformation (LFT) form by including uncertainties and varying parameters with minimal number of repetitions. Uncertain Linear Time Invariant (LTI) and uncertain Linear Parameter-Varying (LPV) controllers can then be synthesized and analyzed in a straightforward way. The authors present in this article a tutorial, that can be downloaded at https://nextcloud.isae.fr/index.php/s/XDfRfHntejHTmmp, to show how to deal with an end-to-end robust design of a spacecraft mission and to provide to researchers a benchmark to test their own algorithms.

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arXiv2022

Advances in Fine Line-Of-Sight Control for Large Space Flexible Structures

The increased need in pointing performance for Earth observation and science Space missions together with the use of lighter and flexible structures directly come with the need of a robust pointing performance budget from the very beginning of the mission design. An extensive understanding of the system physics and its uncertainties is then necessary in order to push control design to the limits of performance and constrains the choice of the set of sensors and actuators. A multi-body framework, the TITOP approach, is used to build all the elementary flexible bodies and mechanisms involved in a fine pointing mission. This framework allows the authors to easily include all system dynamics with an analytical dependency on varying and uncertain mechanical parameters in a unique Linear Fractional Transformation model. This approach opens the doors to modern robust control techniques that robustly guarantee the expected fine pointing requirements. A novel control architecture is proposed to reduce the microvibrations induced both by reaction wheel imbalances and Solar Array Drive Mechanism driving signal, by letting them work during the imaging phase. Thanks to a set of accelerometers placed at the isolated base of the payload and in correspondence of the mirrors with the largest size in a Space telescope (typically the primary and secondary ones), it is possible to estimate the line-of-sight error at the payload level by hybridizing them with the low-frequency measurements of the camera. While a classical Fast Steering Mirror in front of the camera can compensate for a large amount of microvibration, an innovative architecture with a set of six Proof-Mass Actuators installed at the payload isolator level can further improve the pointing performance.

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arXiv2022

Modeling, robust control synthesis and worst-case analysis for an on-orbit servicing mission with large flexible spacecraft

This paper outlines a complete methodology for modeling an on-orbit servicing mission scenario and designing a feedback control system for the attitude dynamics that is guaranteed to robustly meet pointing requirements, despite model uncertainties as well as large inertia and flexibility changes throughout the mission scenario. A model of the uncertain plant was derived, which fully captures the dynamics and couplings between all subsystems as well as the decoupled/coupled configurations of the chaser/target system in a single linear fractional representation (LFR). In addition, a new approach is proposed to model and analyze a closed-loop kinematic chain formed by the chaser and the target spacecraft through the chaser's robotic arm, which uses two local spring-damper systems with uncertain damping and stiffness. This approach offers the possibility to model the dynamical behaviour of a docking mechanism with dynamic stiffness and damping. The controller was designed by taking into account all the interactions between subsystems and uncertainties as well as the time-varying and coupled flexible dynamics. Lastly, the robust stability and worst-case performances were assessed by means of a structured singular value analysis.

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arXiv2022

Sub-Structuring Modeling of Large Space Truss Structures for Structure/Control Optimization in Presence of Parametric Uncertainties

Modern and future high precision pointing space missions face increasingly high challenges related to the widespread use of large flexible structures. The development of new modeling tools which are able to account for the multidisciplinary nature of this problem becomes extremely relevant in order to meet both structure and control performance criteria. This paper proposes a novel methodology to analytically model large truss structures in a sub-structuring framework. A three dimensional unit cube element has been designed and validated with a Finite Element commercial software. This model is composed by multiple two-dimensional sub-mechanisms assembled using block-diagram models. This constitutes the building block for constructing complex truss structures by repetitions of the element. The accurate vibration description of the system and its minimal representation, as well as the possibility of accounting for parametric uncertainties in its mechanical parameters, make it an appropriate tool to perform robust Structure/Control co-design. In order to demonstrate the strengths of the proposed approach, a co-design study case is proposed by combining a multidisciplinary optimization approach based on particle swarm algorithm and multiple structured robust Hinf-synthesis. This has been used to optimize the pointing performances of an high pointing antenna, minimizing the perturbations coming from the Solar Array Mechanisms (SADM) of two solar panels, performing active control by means of multiple proof mass actuators, and simultaneously reduce the mass of the truss-structure which connects the antenna to the main spacecraft body.

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arXiv2021

Robust line-of-sight pointing control on-board a stratospheric balloon-borne platform

This paper addresses the lack of a general methodology for the controller synthesis of an optical instrument on-board a stratospheric balloon-borne platform, such as a telescope or siderostat, to meet pointing requirements that are becoming more and more stringent in the context of astronomy missions. Most often in the literature, a simple control structure is chosen, and the control gains are tuned empirically based on ground testings. However, due to the large dimensions of the balloon and the flight chain, experimental set-ups only involve the pointing system and the platform, whereas flight experience shows that the pointing performance is essentially limited by the rejection of the natural pendulum-like oscillations of the fully deployed system. This observation justifies the need for a model that predicts such flight conditions that cannot be replicated in laboratory, and for an adequate methodology addressing the line-of-sight controller design. In particular, it is necessary to ensure robust stability and performance to the parametric uncertainties inherent to balloon-borne systems, such as complex balloon's properties or release of ballast throughout the flight, especially since experimental validation is limited. In this paper, a dynamical model of the complete system is proposed, based on a multibody approach and accounting for parametric uncertainties with Linear Fractional Transformations. The comparison with flight data shows that the frequency content of the platform's motion is accurately predicted. Then, the robust control of the line-of-sight is tackled as a $\mathcal H_{\infty}$ problem that allows to reach the performance objectives in terms of disturbance rejection, control bandwidth and actuators limitations.

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arXiv2021

Linear Fractional Transformation modeling of multibody dynamics around parameter-dependent equilibrium

This paper proposes a new Linear Fractional Transformation (LFT) modeling approach for uncertain Linear Parameter Varying (LPV) multibody systems with parameter-dependent equilibrium. Traditional multibody approaches, which consist in building the nonlinear model of the whole structure and linearizing it around equilibrium after a numerical trimming, do not allow to isolate parametric variations with the LFT form. Although additional techniques, such as polynomial fitting or symbolic linearization, can provide an LFT model, they may be time-consuming or miss worst-case configurations. The proposed approach relies on the trimming and linearization of the equations at the substructure level, before assembly of the multibody structure, which allows to only perform operations that preserve the LFT form throughout the linearization process. Since the physical origin of the parameters is retained, the linearized LFT-LPV model of the structure exactly covers all plants, in a single parametric model, without introducing conservatism or fitting errors. An application to the LFT-LPV modeling of a robotic arm is proposed; in its nominal configuration, the model obtained with the proposed approach matches the model provided by the software Simscape Multibody, but it is enhanced with parametric variations with the LFT form; a robust LPV synthesis is performed using Matlab robust control toolbox to illustrate the capacity of the proposed approach for control design.

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arXiv2021

Worst-Case Pointing Performance Analysis for Large Flexible Spacecraft

This paper presents a tool, PELIB, developed in MATLAB /SIMULINK environment to perform pointing performance analysis based on European pointing standards. PELIB is designed as an extension of the Satellite Dynamics Toolbox (SDT), which derives the Linear Fractional Transformation (LFT) models of flexible space structures. The addition of PELIB will allow the users of SDT to perform pointing performance analysis of real mission scenarios in the same environment used for control synthesis. PELIB offers as well the possibility to take into account uncertainties in the system. This feature represents an enhancement to the current verification tools available in the European space industry community by providing the worst-case pointing budget. The capabilities of PELIB were demonstrated in a case study involving a spacecraft model with two flexible solar arrays. Several error sources, as well as uncertain parameters, were included in this model. The nominal performance has been investigated using PELIB and compared with the current European reference tool. The worst-case performance is also investigated with the new feature of PELIB to obtain the worst-case performance budget

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arXiv2021

Integrated modelling of microvibrations induced by Solar Array Drive Mechanism for worst-case end-to-end analysis and robust disturbance estimation

Modern and future observation Space missions face increasingly more demanding pointing performance requirements. This is accompanied with the development of larger lightweight flexible structures. This paper outlines a methodology for modeling a generic multi-body flexible spacecraft in an end-to-end fashion within the Two-Inputs Two-Outputs Port framework: from disturbance all the way to pointing performance by tacking into account all the uncertainties of each sub-system. A particular focus is dedicated to a novel generic model for Solar Drive Array Mechanisms and its harmonic disturbances produced by the micro-stepping driver and the gearbox imperfections. The proposed model is validated with the on-board telemetries of a European spacecraft. Moreover this paper shows how the proposed model-based approach can be easily used for control design and closed-loop robust performance analysis. Worst-case scenarios of mechanical parameters combination are investigated to provide robust performance certificate of the reference study case. A Linear Parameter-Varying observer, scheduled by the solar array rotor angle, is finally proposed in order to estimate the disturbance torques induced by the gearbox imperfections just using the measurements coming from a classical attitude control system: a star tracker and a gyrometer.

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arXiv2020

Structure-preserving discretization of port-Hamiltonian plate models

Methods for discretizing port-Hamiltonian systems are of interest both for simulation and control purposes. Despite the large literature on mixed finite elements, no rigorous analysis of the connections between mixed elements and port-Hamiltonian systems has been carried out. In this paper we demonstrate how existing methods can be employed to discretize dynamical plate problems in a structure-preserving way. Based on convergence results of existing schemes, new error estimates are conjectured; numerical simulations confirm the expected behaviors.

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arXiv2018

Port-Hamiltonian formulation and symplectic discretization of Plate models. Part I : Mindlin model for thick plates

The port-Hamiltonian formulation is a powerful method for modeling and interconnecting systems of different natures. In this paper, the port-Hamiltonian formulation in tensorial form of a thick plate described by the Mindlin-Reissner model is presented. Boundary control and observation are taken into account. Thanks to tensorial calculus, it can be seen that the Mindlin plate model mimics the interconnection structure of its one-dimensional counterpart, i.e. the Timoshenko beam. The Partitioned Finite Element Method (PFEM) is then extended to both the vectorial and tensorial formulations in order to obtain a suitable, i.e. structure-preserving, finite-dimensional port-Hamiltonian system (PHs), which preserves the structure and properties of the original distributed parameter system. Mixed boundary conditions are finally handled by introducing some algebraic constraints. Numerical examples are finally presented to validate this approach.

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