arXiv subjects

Lorenzo Fagiano

Publications and source records attributed to Lorenzo Fagiano.

At least 19 recordsLinked to original sources

arXiv2025

Variable L0 Guidance Strategy: Enlarged Operational Envelope and Path-Following

This paper presents a geometric and theoretical study of an exponentially varying look-ahead parameter for UAV path-following guidance. Conventional guidance laws with a fixed look-ahead distance often drive the vehicle into turn-rate saturation when the heading or cross-track error is large, leading to constrained maneuvers and higher control effort. The proposed variable L0 strategy reshapes the look-ahead profile so that the guidance command adapts to the evolving tracking error geometry. A detailed investigation shows that this adaptation significantly enlarges the region in which the commanded turn rate remains unsaturated, allowing the vehicle to operate smoothly over a broader range of error conditions. For representative settings, the unsaturated operational envelope increases by more than 70% relative to the constant L0 formulation. These geometric insights translate to smoother trajectories, earlier recovery from saturation, and reduced control demand. Simulation studies on straight-line and elliptical paths demonstrate the merits of the variable look-ahead strategy, highlighting its control-efficient and reliable path-following performance.

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arXiv2025

Koopman-Based Dynamic Environment Prediction for Safe UAV Navigation

This paper presents a Koopman-based model predictive control (MPC) framework for safe UAV navigation in dynamic environments using real-time LiDAR data. By leveraging the Koopman operator to linearly approximate the dynamics of surrounding objets, we enable efficient and accurate prediction of the position of moving obstacles. Embedding this into an MPC formulation ensures robust, collision-free trajectory planning suitable for real-time execution. The method is validated through simulation and ROS2-Gazebo implementation, demonstrating reliable performance under sensor noise, actuation delays, and environmental uncertainty.

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arXiv2025

SAGE: A Set-based Adaptive Gradient Estimator

A new paradigm to estimate the gradient of a black-box scalar function is introduced, considering it as a member of a set of admissible gradients that are computed using existing function samples. Results on gradient estimate accuracy, derived from a multivariate Taylor series analysis, are used to express the set of admissible gradients through linear inequalities. An approach to refine this gradient estimate set to a desired precision is proposed as well, using an adaptive sampling approach. The resulting framework allows one to estimate gradients from data sets affected by noise with finite bounds, to provide the theoretical best attainable gradient estimate accuracy, and the optimal sampling distance from the point of interest to achieve the best refinement of the gradient set estimates. Using these results, a new algorithm is proposed, named Set-based Adaptive Gradient Estimator (SAGE), which features both sample efficiency and robustness to noise. The performance of SAGE are demonstrated by comparing it with commonly-used and latest gradient estimators from literature and practice, in the context of numerical optimization with a first-order method. The results of an extensive statistical test show that SAGE performs competitively when faced with noiseless data, and emerges as the best method when faced with high noise bounds where other gradient estimators result in large errors.

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arXiv2025

ROBBO: An Efficient Method for Pareto Front Estimation with Guaranteed Accuracy

A new method to estimate the Pareto Front (PF) in bi-objective optimization problems is presented. Assuming a continuous PF, the approach, named ROBBO (RObust and Balanced Bi-objective Optimization), needs to sample at most a finite, pre-computed number of PF points. Upon termination, it guarantees that the worst-case approximation error lies within a desired tolerance range, predefined by the decision maker, for each of the two objective functions. Theoretical results are derived, about the worst-case number of PF samples required to guarantee the wanted accuracy, both in general and for specific sampling methods from the literature. A comparative analysis, both theoretical and numerical, demonstrates the superiority of the proposed method with respect to popular ones. The approach is finally showcased in a constrained path-following problem for a 2-axis positioning system and in a steady-state optimization problem for a Continuous-flow Stirred Tank Reactor. An open demo implementation of ROBBO is made available online.

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arXiv2024

Optimal feature rescaling in machine learning based on neural networks

This paper proposes a novel approach to improve the training efficiency and the generalization performance of Feed Forward Neural Networks (FFNNs) resorting to an optimal rescaling of input features (OFR) carried out by a Genetic Algorithm (GA). The OFR reshapes the input space improving the conditioning of the gradient-based algorithm used for the training. Moreover, the scale factors exploration entailed by GA trials and selection corresponds to different initialization of the first layer weights at each training attempt, thus realizing a multi-start global search algorithm (even though restrained to few weights only) which fosters the achievement of a global minimum. The approach has been tested on a FFNN modeling the outcome of a real industrial process (centerless grinding).

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arXiv2024

On the Kite-Platform Interactions in Offshore Airborne Wind Energy Systems: Frequency Analysis and Control Approach

This study investigates deep offshore, pumping Airborne Wind Energy systems, focusing on the kite-platform interaction. The considered system includes a 360 m2 soft-wing kite, connected by a tether to a winch installed on a 10-meter-deep spar with four mooring lines. Wind power is converted into electricity with a feedback controlled periodic trajectory of the kite and corresponding reeling motion of the tether. An analysis of the mutual influence between the platform and the kite dynamics, with different wave regimes, reveals a rather small sensitivity of the flight pattern to the platform oscillations; on the other hand, the frequency of tether force oscillations can be close to the platform resonance peaks, resulting in possible increased fatigue loads and damage of the floating and submerged components. A control design procedure is then proposed to avoid this problem, acting on the kite path planner. Simulation results confirm the effectiveness of the approach.

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arXiv2023

Model Predictive Control for Multi-Agent Systems under Limited Communication and Time-Varying Network Topology

In control system networks, reconfiguration of the controller when agents are leaving or joining the network is still an open challenge, in particular when operation constraints that depend on each agent's behavior must be met. Drawing our motivation from mobile robot swarms, in this paper, we address this problem by optimizing individual agent performance while guaranteeing persistent constraint satisfaction in presence of bounded communication range and time-varying network topology. The approach we propose is a model predictive control (MPC) formulation, building on multi-trajectory MPC (mt-MPC) concepts. To enable plug and play operations when the system is in closed-loop without the need of a request, the proposed MPC scheme predicts two different state trajectories in the same finite horizon optimal control problem. One trajectory drives the system to the desired target, assuming that the network topology will not change in the prediction horizon, while the second one ensures constraint satisfaction assuming a worst-case scenario in terms of new agents joining the network in the planning horizon. Recursive feasibility and stability of the closed-loop system during plug and play operations are shown. The approach effectiveness is illustrated with a numerical simulation.

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arXiv2023

Multi-agent Distributed Model Predictive Control with Connectivity Constraint

In cooperative multi-agent robotic systems, coordination is necessary in order to complete a given task. Important examples include search and rescue, operations in hazardous environments, and environmental monitoring. Coordination, in turn, requires simultaneous satisfaction of safety critical constraints, in the form of state and input constraints, and a connectivity constraint, in order to ensure that at every time instant there exists a communication path between every pair of agents in the network. In this work, we present a model predictive controller that tackles the problem of performing multi-agent coordination while simultaneously satisfying safety critical and connectivity constraints. The former is formulated in the form of state and input constraints and the latter as a constraint on the second smallest eigenvalue of the associated communication graph Laplacian matrix, also known as Fiedler eigenvalue, which enforces the connectivity of the communication network. We propose a sequential quadratic programming formulation to solve the associated optimization problem that is amenable to distributed optimization, making the proposed solution suitable for control of multi-agent robotics systems relying on local computation. Finally, the effectiveness of the algorithm is highlighted with a numerical simulation.

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arXiv2022

SMGO-$Δ$: Balancing Caution and Reward in Global Optimization with Black-Box Constraints

In numerous applications across all science and engineering areas, there are optimization problems where both the objective function and the constraints have no closed-form expression or are too complex to be managed analytically, that they can only be evaluated through experiments. To address such issues, we design a global optimization technique for problems with black-box objective and constraints. Assuming Lipschitz continuity of the cost and constraint functions, a Set Membership framework is adopted to build a surrogate model of the optimization program, that is used for exploitation and exploration routines. The resulting algorithm, named Set Membership Global Optimization With Black-Box Constraints (SMGO-$Δ$), features one tunable risk parameter, which the user can intuitively adjust to trade-off safety, exploitation, and exploration. The theoretical properties of the algorithm are derived, and the optimization performance is compared with representative techniques from the literature in several benchmarks. Lastly, it is tested and compared with constrained Bayesian optimization in a case study pertaining to model predictive control tuning for a servomechanism with disturbances and plant uncertainties, addressing practically-motivated task-level constraints.

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arXiv2021

An optimal reeling control strategy for pumping airborne wind energy systems without wind speed feedback

Pumping airborne wind energy (AWE) systems employ a kite to convert wind energy into electricity, through a cyclic reeling motion of the tether. The problem of computing the optimal reeling speed for the sake of maximizing the average cycle power is considered. The difficulty stems from two aspects: 1) the uncertain, time- (and space-) varying nature of wind speed, which can not be measured accurately, and 2) the need to consider, in the same optimization problem, the different operational phases of the power cycle. A new, model-based approach that solves this problem is proposed. In the design phase, a model of the AWE system is employed to collect data pertaining to the cycle power obtained with various reel-in/reel-out speed pairs, assuming known wind speed. Then, a nonlinear map, identified from these data, is used as cost function in an optimization program that computes the best reel-in and -out speed pairs for each wind speed. Finally, the optimization results are exploited to infer the link between optimal reeling speed and tether force, which are both measured with high accuracy. Such a link is used to design a feedback controller that computes the reeling speed based on the measured tether force, in order to converge on the optimal force-speed manifold. Simulation results with a realistic model illustrate the effectiveness of the approach.

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arXiv2021

SMGO: A Set Membership Approach to Data-Driven Global Optimization

Many science and engineering applications feature non-convex optimization problems where the objective function can not be handled analytically, i.e. it is a black box. Examples include design optimization via experiments, or via costly finite elements simulations. To solve these problems, global optimization routines are used. These iterative techniques must trade-off exploitation close to the current best point with exploration of unseen regions of the search space. In this respect, a new global optimization strategy based on a Set Membership (SM) framework is proposed. Assuming Lipschitz continuity of the cost function, the approach employs SM concepts to decide whether to switch from an exploitation mode to an exploration one, and vice-versa. The resulting algorithm, named SMGO (Set Membership Global Optimization) is presented. Theoretical properties regarding convergence and computational complexity are derived, and implementation aspects are discussed. Finally, the SMGO performance is evaluated on a set of benchmark non-convex problems and compared with those of other global optimization approaches.

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arXiv2021

Robust multi-rate predictive control using multi-step prediction models learned from data

This note extends a recently proposed algorithm for model identification and robust MPC of asymptotically stable, linear time-invariant systems subject to process and measurement disturbances. Independent output predictors for different steps ahead are estimated with Set Membership methods. It is here shown that the corresponding prediction error bounds are the least conservative in the considered model class. Then, a new multi-rate robust MPC algorithm is developed, employing said multi-step predictors to robustly enforce constraints and stability against disturbances and model uncertainty, and to reduce conservativeness. A simulation example illustrates the effectiveness of the approach.

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arXiv2020

LiDAR-Based Navigation of Tethered Drone Formations in an Unknown Environment

The problem of navigating a formation of interconnected tethered drones, named STEM (System of TEthered Multicopters), in an unknown environment is considered. The tethers feed electrical power from a ground station to the drones and also serve as communication links. The presence of more than one interconnected drone provides enough degrees of freedom to navigate in a cluttered area. The leader drone in the formation must reach a given point of interest, while the followers must move accordingly, avoiding interference with the obstacles. The challenges are the uncertainty in the environment, with obstacles of unknown shape and position, the use of LiDAR (Light Detection And Ranging) sensors, providing only partial information of the surroundings of each drone, and the presence of the tethers, which must not impact with the obstacles and pose additional constraints to how the drones can move. To cope with these problems, a novel real-time planning algorithm based on numerical optimization is proposed: the reference position of each drone is chosen in a centralized way via a convex program, where the LiDAR scans are used to approximate the free space and the drones are moved towards suitably defined intermediate goals in order to eventually reach the point of interest. The approach is successfully tested in numerical simulations with a realistic model of the system.

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arXiv2020

Hierarchical routing control in discrete manufacturing plants via model predictive path allocation and greedy path following

The problem of real-time control and optimization of components' routing in discrete manufacturing plants, where distinct items must undergo a sequence of jobs, is considered. This problem features a large number of discrete control inputs and the presence of temporal-logic constraints. A new approach is proposed, adopting a shift of perspective with respect to previous contributions, from a Eulerian system model that tracks the state of plant nodes, to a Lagrangian model that tracks the state of each part being processed. The approach features a hierarchical structure. At a higher level, a predictive receding horizon strategy allocates a path across the plant to each part in order to minimize a chosen cost criterion. At a lower level, a path following logic computes the control inputs in order to follow the assigned path, while satisfying all constraints. The approach is tested here in simulations, reporting extremely good performance as measured by closed-loop cost function values and computational efficiency, also with very large prediction horizon values. These features pave the way to a number of subsequent research steps, which will culminate with the experimental testing on a pilot plant.

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arXiv2020

Data-driven filtering for linear systems using Set Membership multistep predictors

This paper presents a novel data-driven, direct filtering approach for unknown linear time-invariant systems affected by unknown-but-bounded measurement noise. The proposed technique combines independent multistep prediction models, identified resorting to the Set Membership framework, to refine a set that is guaranteed to contain the true system output. The filtered output is then computed as the central value in such a set. By doing so, the method achieves an accurate output filtering and provides tight and minimal error bounds with respect to the true system output. To attain these results, the online solution of linear programs is required. A modified filtering approach with lower online computational cost is also presented, obtained by moving the solution of the optimization problems to an offline preliminary phase, at the cost of larger accuracy bounds. The performance of the proposed approaches are evaluated and compared with those of standard model-based filtering techniques in a numerical example.

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arXiv2020

Control of a Rigid Wing Pumping Airborne Wind Energy System in all Operational Phases

The control design of an airborne wind energy system with rigid aircraft, vertical take-off and landing, and pumping operation is described. A hierarchical control structure is implemented, in order to address all operational phases: take-off, transition to power generation, pumping energy generation cycles, transition to hovering, and landing. Control design at all hierarchical levels is described. The design approach is conceived and developed with real-world applicability as main driver. Aircraft design considerations in light of system maneuverability are presented, too, as well as three possible alternative strategies for the retraction phase of the pumping cycle. The automatic control approach is assessed in simulation with a realistic model of the overall system, and the results yield a comparison among the three retraction strategies, clearly indicating the most efficient one. The presented results allow one to simulate the dynamical behavior of an AWE system in all operational phases, enabling further studies on all-round system automation, towards fully autonomous and reliable operation.

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arXiv2020

Set Membership identification of linear systems with guaranteed simulation accuracy

The problem of model identification for linear systems is considered, using a finite set of sampled data affected by a bounded measurement noise, with unknown bound. The objective is to identify one-step-ahead models and their accuracy in terms of worst-case simulation error bounds. To do so, the Set Membership identification framework is exploited. Theoretical results are derived, allowing one to estimate the noise bound and system decay rate. Then, these quantities and the data are employed to define the Feasible Parameter Set (FPS), which contains all possible models compatible with the available information. Here, the estimated decay rate is used to refine the standard FPS formulation, by adding constraints that enforce the desired converging behavior of the models' impulse response. Moreover, guaranteed simulation error bounds for an infinite future horizon are derived, improving over recent results pertaining to finite simulation horizon only. These bounds are the basis for a result and method to guarantee asymptotic stability of the identified model. Finally, the desired one-step-ahead model is identified by means of numerical optimization, and the related simulation error bounds are evaluated. Both input-output and state-space model structures are addressed. The approach is showcased on a numerical example and on real-world experimental data of the roll rate dynamics of an autonomous glider.

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arXiv2019

Scenario optimization for optimal training of Echo State Networks

Echo State Networks (ESNs) are widely-used Recurrent Neural Networks. They are dynamical systems including, in state-space form, a nonlinear state equation and a linear output transformation. The common procedure to train ESNs is to randomly select the parameters of the state equation, and then to estimate those of the output equation via a standard least squares problem. Such a procedure is repeated for different instances of the random parameters characterizing the state equation, until satisfactory results are achieved. However, this trial-and-error procedure is not systematic and does not provide any guarantee about the optimality of the identification results. To solve this problem, we propose to complement the identification procedure of ESNs by applying results in scenario optimization. The resulting training procedure is theoretically sound and allows one to link precisely the number of identification instances to a guaranteed optimality bound on relevant performance indexes, such as the Root Mean Square error and the FIT index of the estimated model evaluated over a validation data-set. The proposed procedure is finally applied to the simulated model of a pH neutralization process: the obtained results confirm the validity of the approach.

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