arXiv subjects

Daniele Astolfi

Publications and source records attributed to Daniele Astolfi.

At least 19 recordsLinked to original sources

arXiv2026

Global Convergence of Control-Based Lagrangian Flows for Non-Convex Optimization

This paper studies the continuous-time dynamics generated by control-theoretic Lagrangian methods for equality-constrained optimization. In particular, we consider dynamics induced by proportional-integral and feedback linearization controllers, which have recently been proposed as alternatives to primal-dual gradient methods. Unlike global convergence results for these dynamics, which rely on strong convexity of the objective function or boundedness assumptions, we exploit the geometric structure induced by the constraints. Specifically, we show global exponential convergence for non-convex problems that satisfy a suitable convexity property when restricted to the constraint manifold.

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arXiv2026

On the Solvability of Quasi-Regulator Equations in Non-smooth Output Regulation

Motivated by the prevalence of non-smooth, possibly non-periodic signals in real-world applications, the output regulation of linear systems subject to non-smooth non-periodic exogenous signals has emerged as a challenging problem. A fundamental prerequisite for solving this problem is the existence of solutions to the so-called ``quasi-regulator equations''. In this paper, we investigate the solvability of these equations. To this end, we reformulate the quasi-regulator equations as differential-algebraic equations and highlight the critical role played by the system's relative degree. We finally propose a ``non-smooth non-resonance condition'' that, under specific relative degree requirements, provides a necessary and sufficient characterization of the solvability of the quasi-regulator equations.

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arXiv2026

Learning a Contracting KKL-observer with Local Optimal Guarantees

The Kazantzis-Kravaris-Luenberger (KKL) observer provides a general framework for nonlinear state estimation by immersing the system dynamics into a stable linear or nonlinear latent dynamics. However, the performance of KKL observers relies heavily on the specific choice of these latent dynamics, which is often heuristic. This paper proposes a methodology to learn a KKL observer that combines global stability guarantees with local optimality. We derive a condition on the latent dynamics such that the observer locally mimics the behavior of a Minimum Energy Estimator (Mortensen observer). We then employ Deep Learning to approximate the KKL transformation and the latent dynamics, using neural network architectures that structurally enforce the contraction property. The proposed strategy is validated through numerical simulations on nonlinear benchmarks, demonstrating a good performance in the presence of state and measurement noise.

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arXiv2026

A Nonlinear Incremental Approach for Replay Attack Detection

Replay attacks comprise replaying previously recorded sensor measurements and injecting malicious signals into a physical plant, causing great damage to cyber-physical systems. Replay attack detection has been widely studied for linear systems, whereas limited research has been reported for nonlinear cases. In this paper, the replay attack is studied in the context of a nonlinear plant controlled by an observer-based output feedback controller. We first analyze replay attack detection using an innovation-based detector and reveal that this detector alone may fail to detect such attacks. Consequently, we turn to a watermark-based design framework to improve the detection. In the proposed framework, the effects of the watermark on attack detection and closed-loop system performance loss are quantified by two indices, which exploit the incremental gains of nonlinear systems. To balance the detection performance and control system performance loss, an explicit optimization problem is formulated. Moreover, to achieve a better balance, we generalize the proposed watermark design framework to co-design the watermark, controller and observer. Numerical simulations are presented to validate the proposed frameworks.

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arXiv2025

Integral action for bilinear systems with application to counter current heat exchanger

In this study, we propose a robust control strategy for a counter-current heat exchanger. The primary objective is to regulate the outlet temperature of one fluid stream by manipulating the flow rate of the second counter-current fluid stream. By leveraging the energy balance equations, we develop a structured bilinear system model derived by using a uniform spatial discretization of each stream into a cascade of homogeneous volumes and by considering the heat transfer and convective phenomena within the exchanger. We introduce two control strategies: (i) an output feedback controller incorporating a state observer and (ii) a purely integral control law. The effectiveness of the proposed control strategy is validated through real experiments on a real heat exchanger.

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arXiv2025

Output Regulation of Linear Systems with Non-periodic Non-smooth Exogenous Signals

We address the output regulation problem of linear systems with non-smooth and non-periodic exogenous signals. Specifically, we first formulate and solve the full-information problem by designing a state-feedback controller. We study the solvability of the regulator equations, providing a new non-resonance condition. We then focus on the error-feedback problem, for which we design a (non-robust) internal model leveraging the concept of canonical realisation and applying a high-gain method for the stabilisation of the closed-loop system under the minimum-phase assumption. Finally, we study the regulation problem involving model parameter uncertainties. Drawing ideas from both hybrid and time-varying (smooth) output regulation, we propose two methods to establish an internal model that is robust to uncertainties. The first method is an extension of the hybrid internal model, while the second relies on a new concept of immersion. In this non-smooth case, the immersion is established based on integrals rather than derivatives. The effectiveness of the proposed solutions is illustrated by a circuit regulation example.

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arXiv2025

Steady-State Cascade Operators and their Role in Linear Control, Estimation, and Model Reduction Problems

Certain linear matrix operators arise naturally in systems analysis and design problems involving cascade interconnections of linear time-invariant systems, including problems of stabilization, estimation, and model order reduction. We conduct here a comprehensive study of these operators and their relevant system-theoretic properties. The general theory is leveraged to delineate both known and new design methodologies for control and observation of cascades, and to characterize structural properties of reduced models. Several entirely new designs arise from this systematic categorization, including new recursive and low-gain design frameworks for observation of cascaded systems. The benefits of the results beyond the linear time-invariant setting are demonstrated through preliminary extensions for nonlinear systems, with an outlook towards the development of a similarly comprehensive nonlinear theory.

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arXiv2024

Edges' Riemannian energy analysis for synchronization of multi-agent nonlinear systems over undirected weighted graphs

In this note we investigate the problem of global exponential synchronization of multi-agent systems described by nonlinear input affine dynamics. We consider the case of networks described by undirected connected graphs possibly without leader. We present a set of sufficient conditions based on a Riemannian metric approach in order to design a state-feedback distributed control law. Then, we study the convergence properties of the overall network. By exploiting the properties of the edge Laplacian we construct a Lyapunov function that allows to conclude global exponential synchronization of the overall network.

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arXiv2024

Generalized Lyapunov conditions for k-contraction: analysis and feedback design

Recently, the concept of k-contraction has been introduced as a promising generalization of contraction for dynamical systems. However, the study of k-contraction properties has faced significant challenges due to the reliance on complex mathematical objects called matrix compounds. As a result, related control design methodologies have yet to appear in the literature. In this paper, we overcome existing limitations and propose new sufficient conditions for k-contraction which do not require matrix compounds computation. Notably, these conditions are also necessary in the linear time-invariant framework. Leveraging on these findings, we propose a feedback design methodology for both the linear and the nonlinear scenarios which can be used to enforce k-contractivity properties on the closed-loop dynamics.

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arXiv2024

Integral action feedback design for conservative abstract systems in the presence of input nonlinearities

In this article, we present a stabilization feedback law with integral action for conservative abstract linear systems subjected to actuator nonlinearity. Based on the designed control law, we first prove the well-posedness and global asymptotic stability of the origin of the closed-loop system by constructing a weak Lyapunov functional. Secondly, as an illustration, we apply the results to a wave equation coupled with an ordinary differential equation (ODE) at the boundary. Finally, we give the simulation results to illustrate the effectiveness of our method.

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arXiv2024

Chaotic Masking Protocol for Secure Communication and Attack Detection in Remote Estimation of Cyber-Physical Systems

In remote estimation of cyber-physical systems (CPSs), sensor measurements transmitted through network may be attacked by adversaries, leading to leakage risk of privacy (e.g., the system state), and/or failure of the remote estimator. To deal with this problem, a chaotic masking protocol is proposed in this paper to secure the sensor measurements transmission. In detail, at the plant side, a chaotic dynamic system is deployed to encode the sensor measurement, and at the estimator side, an estimator estimates both states of the physical plant and the chaotic system. With this protocol, no additional secure communication links is needed for synchronization, and the masking effect can be perfectly removed when the estimator is in steady state. Furthermore, this masking protocol can deal with multiple types of attacks, i.e., eavesdropping attack, replay attack, and stealthy false data injection attack.

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arXiv2022

Total stability and integral action for discrete-time nonlinear systems

Robustness guarantees are important properties to be looked for during control design. They ensure stability of closed-loop systems in face of uncertainties, unmodeled effects and bounded disturbances. While the theory on robust stability is well established in the continuous-time nonlinear framework, the same cannot be stated for its discrete-time counterpart. In this paper, we propose the discrete-time parallel of total stability results for continuous-time nonlinear system. This enables the analysis of robustness properties via simple model difference in the discrete-time context. First, we study how existence of equilibria for a nominal model transfers to sufficiently similar ones. Then, we provide results on the

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arXiv2022

ISS-Lyapunov strictification via observer design and integral action control for a Korteweg-de-Vries equation

The article deals with the output regulation of a Korteweg-de-Vries (KdV) system subject to a distributed disturbance. The control input and the output are located at the boundary. To achieve this objective, we follow a Lyapunov approach. For that, inspired by the strictication methodology proposed in [42] in the finite-dimensional context, we construct an ISS-Lyapunov functional for the KdV equation thanks to the use of an observer designed via the backstepping approach. Then, thanks to this Lyapunov functional, we apply the forwarding method in order to solve the desired output regulation problem.

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arXiv2021

Forwarding-Lyapunov design for the stabilization of coupled ODEs and exponentially stable PDEs

This paper is about the stabilization of a cascade system composed by an infinite-dimensional system, that we suppose to be exponentially stable, and an ordinary differential equation (ODE), that we suppose to be marginally stable. The system is controlled through the infinite-dimensional system. Such a structure is particularly useful when applying the internal model approach on infinite-dimensional systems. Our strategy relies on the forwarding method, which uses a Lyapunov functional and a Sylvester equation to build a feedback-law. Under some classical assumptions in the output regulation theory, we prove that the closed-loop system is globally exponentially stable.

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arXiv2021

Nonlinear Robust Periodic Output Regulation of Minimum Phase Systems

In linear systems theory it's a well known fact that a regulator given by the cascade of an oscillatory dynamics, driven by some regulated variables, and of a stabiliser stabilising the cascade of the plant and of the oscillators has the ability of blocking on the steady state of the regulated variables any harmonics matched with the ones of the oscillators. This is the well-celebrated internal model principle. In this paper we are interested to follow the same design route for a controlled plant that is a nonlinear and periodic system with period T : we add a bunch of linear oscillators, embedding n o harmonics that are multiple of 2$π$/T , driven by a "regulated variable" of the nonlinear system, we look for a stabiliser for the nonlinear cascade of the plant and the oscillators, and we study the asymptotic properties of the resulting closedloop regulated variable. In this framework the contributions of the paper are multiple: for specific class of minimum-phase systems we present a systematic way of designing a stabiliser, which is uniform with respect to n o , by using a mix of high-gain and forwarding techniques; we prove that the resulting closed-loop system has a periodic steady state with period T with a domain of attraction not shrinking with n o ; similarly to the linear case, we also show that the spectrum of the steady state closed-loop regulated variable does not contain the n harmonics embedded in the bunch of oscillators and that the L 2 norm of the regulated variable is a monotonically decreasing function of n o. The results are robust, namely the asymptotic properties on the regulated variable hold also in presence of any uncertainties in the controlled plant not destroying closed-loop stability.

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arXiv2021

About Robustness of Control Systems Embedding an Internal Model

Robustness is a basic property of any control system. In the context of linear output regulation, it was proved that embedding an internal model of the exogenous signals is necessary and sufficient to achieve tracking of the desired reference signals in spite of external disturbances and parametric uncertainties. This result is commonly known as "internal model principle". A complete extension of such linear result to general nonlinear systems is still an open problem, which is exacerbated by the large number of alternative definitions of uncertainty and desired control goals that are possible in a nonlinear setting. In this paper, we develop a general framework in which all these different notions can be formally characterized in a unifying way. Classical results are reinterpreted in the proposed setting, and new results and insights are presented with a focus on robust rejection/tracking of arbitrary harmonic content. Moreover, we show by counter-example that, in the relevant case of continuous unstructured uncertainties, there are problems for which no smooth finite-dimensional robust regulator exists ensuring exact regulation.

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arXiv2021

Forwarding techniques for the global stabilization of dissipative infinite-dimensional systems coupled with an ODE

This paper deals with the stabilization of a coupled system composed by an infinite-dimensional system and an ODE. Moreover, the control, which appears in the dynamics of the ODE, is subject to a general class of nonlinearities. Such a situation may arise, for instance, when the actuator admits a dynamics. The open-loop ODE is exponentially stable and the open-loop infinite-dimensional system is dissipative, i.e., the energy is nonincreasing, but its equilibrium point is not necessarily attractive. The feedback design is based on an extension of a finite-dimensional method, namely the forwarding method. We propose some sufficient conditions that imply the well-posedness and the global asymptotic stability of the closed-loop system. As illustration, we apply these results to a transport equation coupled with an ODE.

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arXiv2020

Forwarding design for stabilization of a coupled transport equation-ODE with a cone-bounded input nonlinearity

We propose a new design technique for the stabilization of coupled ODE-PDE systems in feedforward form. In particular, we address the stabilization problem of a one-dimensional transport equation driven by a scalar ODE which is controlled via a cone-bounded nonlinearity. The unforced transport equation is conservative but not asymptotically stable. The proposed technique is inspired by the forwarding approach early introduced in the 90's. Well-posedness and asymptotic stability of the closed-loop system are discussed.

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