arXiv subjects

Riccardo Bertollo

Publications and source records attributed to Riccardo Bertollo.

5 recordsLinked to original sources

arXiv2026

Incremental Stability and Convergence Properties of Discrete-Time Projected Control Systems

Projection-based controllers can overcome fundamental limitations of classical linear time-invariant control by modifying the controller's input-output behavior via projection. A key example is given by the hybrid integrator-gain system, a projected integrator, which has recently found successful application in several industrial systems. While prior work on analysis and design of projection-based control systems has primarily focused on the continuous-time setting and non-incremental analysis, a more refined incremental analysis in discrete-time is needed to better reflect actual digital implementation and obtain more accurate (robust) performance assessment. To address this need, this paper considers incremental stability and convergence analysis of discrete-time projection-based control systems. Our first methodology is based on showing that such controllers preserve the quadratic incremental stability of their nominal (unprojected) dynamics, if the projection metric is well-designed. Building on this, we derive a small-gain condition guaranteeing incremental input-to-state stability for interconnections of projected controllers with general nonlinear plants. A second approach is grounded in a direct Lyapunov-based method for verifying incremental stability in input-affine piecewise-smooth systems, which can be seen as an extension of the classical discrete-time Demidovic conditions. We illustrate our results through several examples, and demonstrate performance quantification via nonlinear Bode plots, with a special focus on first-order projection elements.

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arXiv2025

A Scenario-based Model Predictive Control Scheme for Pandemic Response through Non-pharmaceutical Interventions

This paper presents a scenario-based model predictive control (MPC) scheme designed to control an evolving pandemic via non-pharmaceutical intervention (NPIs). The proposed approach combines predictions of possible pandemic evolution to decide on a level of severity of NPIs to be implemented over multiple weeks to maintain hospital pressure below a prescribed threshold, while minimizing their impact on society. Specifically, we first introduce a compartmental model which divides the population into Susceptible, Infected, Detected, Threatened, Healed, and Expired (SIDTHE) subpopulations and describe its positive invariant set. This model is expressive enough to explicitly capture the fraction of hospitalized individuals while preserving parameter identifiability w.r.t. publicly available datasets. Second, we devise a scenario-based MPC scheme with recourse actions that captures potential uncertainty of the model parameters. e.g., due to population behavior or seasonality. Our results show that the scenario-based nature of the proposed controller manages to adequately respond to all scenarios, keeping the hospital pressure at bay also in very challenging situations when conventional MPC methods fail.

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arXiv2024

Hybrid Lyapunov-based feedback stabilization of bipedal locomotion based on reference spreading

We propose a hybrid formulation of the linear inverted pendulum model for bipedal locomotion, where the foot switches are triggered based on the center of mass position, removing the need for pre-defined footstep timings. Using a concept similar to reference spreading, we define nontrivial tracking error coordinates induced by our hybrid model. These coordinates enjoy desirable linear flow dynamics and rather elegant jump dynamics perturbed by a suitable extended class ${\mathcal K}_\infty$ function of the position error. We stabilize this hybrid error dynamics using a saturated feedback controller, selecting its gains by solving a convex optimization problem. We prove local asymptotic stability of the tracking error and provide a certified estimate of the basin of attraction, comparing it with a numerical estimate obtained from the integration of the closed-loop dynamics. Simulations on a full-body model of a real robot show the practical applicability of the proposed framework and its advantages with respect to a standard model predictive control formulation.

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arXiv2023

Hybrid coupling rules for leaderless heterogeneous oscillators: uniform global asymptotic and finite-time synchronization

We investigate the engineering scenario where the objective is to synchronize heterogeneous oscillators in a distributed fashion. The internal dynamics of each oscillator are general enough to capture their time-varying natural frequency as well as physical couplings and unknown bounded terms. A communication layer is set in place to allow the oscillators to exchange synchronizing coupling actions through a tree-like leaderless network. In particular, we present a class of hybrid coupling rules depending only on local information to ensure uniform global practical or asymptotic synchronization, which is impossible to obtain by using the Kuramoto model customarily used in the literature. We further show that the synchronization set can be made uniformly globally prescribed finite-time stable by selecting the coupling function to be discontinuous at the origin. Novel mathematical tools on non-pathological functions and set-valued Lie derivatives are developed to carry out the stability analysis. The effectiveness of the approach is illustrated in simulations where we apply our synchronizing hybrid coupling rules to models of power grids previously used in the literature.

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arXiv2022

Distributed Hybrid Observer With Prescribed Convergence Rate for a Linear Plant Using Multi-Hop Decomposition

With a continuous-time formulation of the multihop decomposition, we propose a distributed hybrid observer for a sensor network where the plant and local observers run in continuous time and the information exchange among the sensing nodes is sampled-data. Process disturbances, measurement noise and communication noise are considered, and we prove that under some necessary detectability assumptions the observer gains can be tuned to guarantee exponential ISS with a prescribeda convergence rate. Simulations illustrate the performance of the proposed observer.

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