arXiv subjects

Alessandro Astolfi

Publications and source records attributed to Alessandro Astolfi.

14 recordsLinked to original sources

arXiv2026

Global Exponential Stabilization of the Kinematic Bicycle Model of a Car in Polar Coordinates

At parking speeds, the kinematic bicycle is the prevailing model for car-like vehicles. Yet, despite its wide use, stabilizing feedback laws for this system are scarce in the literature, and existing designs often do not reproduce realistic parking maneuvers. This limitation is inherent to the Cartesian coordinates, where Brockett's condition rules out smooth static feedback stabilization. We bypass this obstruction by transforming the system into polar coordinates together with additional range-normalized coordinates that encode the geometry of human-like parking maneuvers. In the transformed coordinates, the dynamics take a strict-feedback form, enabling a nonconventional backstepping design. We exploit the particular structure to develop smooth feedback laws that achieve global exponential stabilization in the transformed coordinates which in turn generates parking trajectories resembling the one performed by human drivers through feedback alone.

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arXiv2026

Interconnection-based Model Reduction for Linear Hybrid Systems

In this paper, we address the model reduction problem for linear hybrid systems via the interconnection-based technique called moment matching. We consider two classical interconnections, namely the direct and swapped interconnections, in the hybrid setting, and we present families of reduced-order models for each interconnection via a hybrid characterisation of the steady-state responses. By combining the results for each interconnection, the design of a reduced-order model that achieves moment matching simultaneously for both interconnections is studied. In addition, we show that the presented results have simplified counterparts when the jumps of the hybrid system are periodic. A numerical simulation is finally given to illustrate the results.

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arXiv2025

Nonholonomic Robot Parking by Feedback -- Part I: Modular Strict CLF Designs

It has been known in the robotics literature since about 1995 that, in polar coordinates, the nonholonomic unicycle is asymptotically stabilizable by smooth feedback, even globally. We introduce a modular design framework that selects the forward velocity to decouple the radial coordinate, allowing the steering subsystem to be stabilized independently. Within this structure, we develop families of feedback laws using passivity, backstepping, and integrator forwarding. Each law is accompanied by a strict control Lyapunov function, including barrier variants that enforce angular constraints. These strict CLFs provide constructive class KL convergence estimates and enable eigenvalue assignment at the target equilibrium. The framework generalizes and extends prior modular and nonmodular approaches, while preparing the ground for inverse optimal and adaptive redesigns in the sequel paper.

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arXiv2025

Integrator Forwading Design for Unicycles with Constant and Actuated Velocity in Polar Coordinates

In a companion paper, we present a modular framework for unicycle stabilization in polar coordinates that provides smooth steering laws through backstepping. Surprisingly, the same problem also allows the application of integrator forwarding. In this work, we leverage this feature and construct new smooth steering laws together with control Lyapunov functions (CLFs), expanding the set of CLFs available for inverse optimal control design. In the case of constant forward velocity (Dubins car), backstepping produces finite-time (deadbeat) parking, and we show that integrator forwarding yields the very same class of solutions. This reveals a fundamental connection between backstepping and forwarding in addressing both the unicycle and, the Dubins car parking problems.

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arXiv2025

Power-Series Approach to Moment-Matching-Based Model Reduction of MIMO Polynomial Nonlinear Systems

The model reduction problem for high-order multi-input, multi-output (MIMO) polynomial nonlinear systems based on moment matching is addressed. The technique of power-series decomposition is exploited: this decomposes the solution of the nonlinear PDE characterizing the center manifold into the solutions of a series of recursively defined Sylvester equations. This approach allows yielding nonlinear reduced-order models in very much the same way as in the linear case (e.g. analytically). Algorithms are proposed for obtaining the order and the parameters of the reduced-order models with precision of degree $\kappa$. The approach also provides new insights into the nonlinear moment matching problem: first, a lower bound for the order of the reduced-order model is obtained, which, in the MIMO case, can be strictly less than the number of matched moments; second, it is revealed that the lower bound is affected by the ratio of the number of the input and output channels; third, it is shown that under mild conditions, a nonlinear reduced-order model can always be constructed with either a linear state equation or a linear output equation.

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arXiv2024

A polynomial approximation scheme for nonlinear model reduction by moment matching

We propose a procedure for the numerical approximation of invariance equations arising in the moment matching technique associated with reduced-order modeling of high-dimensional dynamical systems. The Galerkin residual method is employed to find an approximate solution to the invariance equation using a Newton iteration on the coefficients of a monomial basis expansion of the solution. These solutions to the invariance equations can then be used to construct reduced-order models. We assess the ability of the method to solve the invariance PDE system as well as to achieve moment matching and recover the steady-state behaviour of nonlinear systems with state dimension of order 1000 driven by linear and nonlinear signal generators.

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arXiv2022

Generation of new exciting regressors for consistent on-line estimation of unknown constant parameters

The problem of parameter estimation from a standard vector linear regression equation in the absence of sufficient excitation in the regressor is addressed. The first step to solve the problem consists in transforming this equation into a set of scalar ones using the well-known dynamic regressor extension and mixing technique. Then a novel procedure to generate new scalar exciting regressors is proposed.} The superior performance of a classical gradient estimator using this new regressor, instead of the original one, is illustrated with comprehensive simulations.

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arXiv2021

Frequency Domain Stability Method for Reset Systems

Today, linear PID controllers cannot satisfy requirements of high-precision industry due to the development of technology. According to the literature, reset controllers can overcome this important barrier. However, similar to other non-linear controllers, stability analysis for these controllers is complex and needs parametric models of the systems. Consequently, the applicability of these controllers may diminish in industry. The well-known Hb method is one of the solutions of this significant problem. Nevertheless, assessing the Hb condition in the frequency-domain is complex, particularly for high dimensional plants. Furthermore, it cannot assess UBIBS stability of reset control systems in the case of reseting to non-zero values. In this paper, the aforementioned problems have been solved for the first and second order reset elements and a frequency-domain approach for assessing stability of reset control systems is developed. Finally, some practical examples are presented to demonstrate the effectiveness of the proposed approach to use the frequency response measurement directly to assess the stability.

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arXiv2020

A Frequency-Domain Stability Method for Reset Systems

Nowadays, the demand for an alternative to linear PID controllers has increased because of the rising expectations of the high-precision industry. The potential of reset controllers to solve this important challenge has been extensively demonstrated in the literature. However, similarly to other non-linear controllers, the stability analysis for these controllers is complex and relies on parametric models of the systems which may hinder the applicability of these controllers in industry. The well-known Hbeta method tries to solve this significant issue. However, assessing the H\b{eta} condition in the frequency-domain is complex, especially for high dimensional plants. In addition, it cannot be used to assess UBIBS stability of reset control systems in the case of reseting to non-zero values. These problems have been solved in this paper for the first order reset elements, and an easy-to-use frequency approach for assessing stability of reset control systems is proposed. The effectiveness of the proposed approach is demonstrated through a practical example.

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arXiv2019

New Results on Parameter Estimation via Dynamic Regressor Extension and Mixing: Continuous and Discrete-time Cases

We present some new results on the dynamic regressor extension and mixing parameter estimators for linear regression models recently proposed in the literature. This technique has proven instrumental in the solution of several open problems in system identification and adaptive control. The new results include: (i) a unified treatment of the continuous and the discrete-time cases; (ii) the proposal of two new extended regressor matrices, one which guarantees a quantifiable transient performance improvement, and the other exponential convergence under conditions that are strictly weaker than regressor persistence of excitation; and (iii) an alternative estimator ensuring parameter estimation in finite-time that retains its alertness to track time-varying parameters. Simulations that illustrate our results are also presented.

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arXiv2018

Orbital Stabilization of Nonlinear Systems via the Immersion and Invariance Technique

Immersion and Invariance is a technique for the design of stabilizing and adaptive controllers and state observers for nonlinear systems. In all these applications the problem considered is the stabilization of equilibrium points. Motivated by some modern applications we show that the technique can also be used to solve the problem of orbital stabilization, where the final objective is to generate periodic solutions that are attractive. The feasibility of our result is illustrated with some classical mechanical engineering and electronics examples.

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arXiv2017

A Convex Optimization Approach for Backstepping PDE Design: Volterra and Fredholm Operators

Backstepping design for boundary linear PDE is formulated as a convex optimization problem. Some classes of parabolic PDEs and a first-order hyperbolic PDE are studied, with particular attention to non-strict feedback structures. Based on the compactness of the Volterra and Fredholm type operators involved, their Kernels are approximated via polynomial functions. The resulting Kernel-PDEs are optimized using Sum-of-Squares(SOS) decomposition and solved via semidefinite programming, with sufficient precision to guarantee the stability of the system in the L2-norm. The effectiveness and limitations of the approach proposed are illustrated by numerical solutions of some Kernel-PDEs.

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arXiv2013

Families of moment matching based, structure preserving approximations for linear port Hamiltonian systems

In this paper we propose a solution to the problem of moment matching with preservation of the port Hamiltonian structure, in the framework of time-domain moment matching. We characterize several families of parameterized port Hamiltonian models that match the moments of a given port Hamiltonian system, at a set of finite interpolation points. We also discuss the problem of Markov parameters matching for linear systems as a moment matching problem for descriptor representations associated to the given system, at zero interpolation points. Solving this problem yields families of parameterized reduced order models that achieve Markov parameter matching. Finally, we apply these results to the port Hamiltonian case, resulting in families of parameterized reduced order port Hamiltonian approximations.

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arXiv2009

Homogeneous Approximation, Recursive Observer Design, and Output Feedback

We introduce two new tools that can be useful in nonlinear observer and output feedback design. The first one is a simple extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting this extension, we give several results concerning stability and robustness for a homogeneous in the bi-limit vector field. The second tool is a new recursive observer design procedure for a chain of integrator. Combining these two tools, we propose a new global asymptotic stabilization result by output feedback for feedback and feedforward systems.

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