arXiv subjects

Andrea Bisoffi

Publications and source records attributed to Andrea Bisoffi.

At least 19 recordsLinked to original sources

arXiv2026

Output regulation via input-output data

From a multi-input-multi-output (MIMO) discrete-time linear system, we collect input-output data affected by noise in the form of an unknown exosignal and, from these data points (without knowledge of the system model), we design a feedback controller that asymptotically annihilates the effect of that exosignal on the output. This amounts to solving an output regulation problem purely from input-output data, for MIMO linear systems. The design of the controller corresponds to a semidefinite program and is pursued on a suitable auxiliary system. Such design carries over from the auxiliary system to the original one by a rigorous examination of the relation between the solutions of the two systems.

math.OC↗

arXiv2025

Event-triggered control of nonlinear systems from data

In a recent paper [8], we introduced a data-based approach to design event-triggered controllers for linear systems directly from data. Here, we extend the results in [8] to a class of nonlinear systems. We provide two data-based designs certified by a (classical) Lyapunov function. For these two designs, we devise event-triggered policies that rely on the previously found Lyapunov function, have parameters tuned from data, ensure a positive minimum inter-event time, and act based either on the state error or on the library error. These two different policies, and their respective advantages, are illustrated numerically.

eess.SY↗

arXiv2024

Data-driven input-to-state stabilization

For the class of nonlinear input-affine systems with polynomial dynamics, we consider the problem of designing an input-to-state stabilizing controller with respect to typical exogenous signals in a feedback control system, such as actuator and process disturbances. We address this problem in a data-based setting when we cannot avail ourselves of the dynamics of the actual system, but only of data generated by it under unknown bounded noise. For all dynamics consistent with data, we derive sum-of-squares programs to design an input-to-state stabilizing controller, an input-to-state Lyapunov function and the corresponding comparison functions. This numerical design for input-to-state stabilization seems to be relevant not only in the considered data-based setting, but also in a model-based setting. Illustration of feasibility of the provided sum-of-squares programs is provided on a numerical example.

math.OC↗

arXiv2024

Controller synthesis for input-state data with measurement errors

We consider the problem of designing a state-feedback controller for a linear system, based only on noisy input-state data. We focus on input-state data corrupted by measurement errors, which, albeit less investigated, are as relevant as process disturbances in applications. For energy and instantaneous bounds on these measurement errors, we derive linear matrix inequalities for controller design where the one for the energy bound is equivalent to robust stabilization of all systems consistent with the noisy data points via a common Lyapunov function.

eess.SY↗

arXiv2024

Setpoint control of bilinear systems from noisy data

We consider the problem of designing a controller for an unknown bilinear system using only noisy input-states data points generated by it. The controller should achieve regulation to a given state setpoint and provide a guaranteed basin of attraction. Determining the equilibrium input to achieve that setpoint is not trivial in a data-based setting and we propose the design of a controller in two scenarios. The design takes the form of linear matrix inequalities and is validated numerically for a Cuk converter.

eess.SY↗

arXiv2024

Controller Synthesis from Noisy-Input Noisy-Output Data

We consider the problem of synthesizing a dynamic output-feedback controller for a linear system, using solely input-output data corrupted by measurement noise. To handle input-output data, an auxiliary representation of the original system is introduced. By exploiting the structure of the auxiliary system, we design a controller that robustly stabilizes all possible systems consistent with data. Notably, we also provide a novel solution to extend the results to generic multi-input multi-output systems. The findings are illustrated by numerical examples.

eess.SY↗

arXiv2023

Data-driven input-to-state stabilization with respect to measurement errors

We consider noisy input/state data collected from an experiment on a polynomial input-affine nonlinear system. Motivated by event-triggered control, we provide data-based conditions for input-to-state stability with respect to measurement errors. Such conditions, which take into account all dynamics consistent with data, lead to the design of a feedback controller, an ISS Lyapunov function, and comparison functions ensuring ISS with respect to measurement errors. When solved alternately for two subsets of the decision variables, these conditions become a convex sum-of-squares program. Feasibility of the program is illustrated with a numerical example.

eess.SY↗

arXiv2021

Data-driven design of safe control for polynomial systems

We consider the problem of designing an invariant set using only a finite set of input-state data collected from an unknown polynomial system in continuous time. We consider noisy data, i.e., corrupted by an unknown-but-bounded disturbance. We derive a data-dependent sum-of-squares program that enforces invariance of a set and also optimizes the size of the invariant set while keeping it within a set of user-defined safety constraints; the solution of this program directly provides a polynomial invariant set and a state-feedback controller. We numerically test the design on a system of two platooning cars.

eess.SY↗

arXiv2021

Learning controllers for performance through LMI regions

In an open-loop experiment, an input sequence is applied to an unknown linear time-invariant system (in continuous or discrete time) affected also by an unknown-but-bounded disturbance sequence (with an energy or instantaneous bound); the corresponding state sequence is measured. The goal is to design directly from the input and state sequences a controller that enforces a certain performance specification on the transient behaviour of the unknown system. The performance specification is expressed through a subset of the complex plane where closed-loop eigenvalues need to belong, a so called LMI region. For this control design problem, we provide here convex programs to enforce the performance specification from data in the form of linear matrix inequalities (LMI). For generic LMI regions, these are sufficient conditions to assign the eigenvalues within the LMI region for all possible dynamics consistent with data, and become necessary and sufficient conditions for special LMI regions. In this way, we extend classical model-based conditions from a seminal work in the literature to the setting of data-driven control from noisy data. Through two numerical examples, we investigate how these data-based conditions compare with each other.

eess.SY↗

arXiv2021

Data-driven control via Petersen's lemma

We address the problem of designing a stabilizing closed-loop control law directly from input and state measurements collected in an open-loop experiment. In the presence of noise in data, we have that a set of dynamics could have generated the collected data and we need the designed controller to stabilize such set of data-consistent dynamics robustly. For this problem of data-driven control with noisy data, we advocate the use of a popular tool from robust control, Petersen's lemma. In the cases of data generated by linear and polynomial systems, we conveniently express the uncertainty captured in the set of data-consistent dynamics through a matrix ellipsoid, and we show that a specific form of this matrix ellipsoid makes it possible to apply Petersen's lemma to all of the mentioned cases. In this way, we obtain necessary and sufficient conditions for data-driven stabilization of linear systems through a linear matrix inequality. The matrix ellipsoid representation enables insights and interpretations of the designed control laws. In the same way, we also obtain sufficient conditions for data-driven stabilization of polynomial systems through (convex) sum-of-squares programs. The findings are illustrated numerically.

eess.SY↗

arXiv2021

Trade-offs in learning controllers from noisy data

In data-driven control, a central question is how to handle noisy data. In this work, we consider the problem of designing a stabilizing controller for an unknown linear system using only a finite set of noisy data collected from the system. For this problem, many recent works have considered a disturbance model based on energy-type bounds. Here, we consider an alternative more natural model where the disturbance obeys instantaneous bounds. In this case, the existing approaches, which would convert instantaneous bounds into energy-type bounds, can be overly conservative. In contrast, without any conversion step, simple arguments based on the S-procedure lead to a very effective controller design through a convex program. Specifically, the feasible set of the latter design problem is always larger, and the set of system matrices consistent with data is always smaller and decreases significantly with the number of data points. These findings and some computational aspects are examined in a number of numerical examples.

eess.SY↗

arXiv2021

Obstacle Avoidance via Hybrid Feedback

In this paper we present a hybrid feedback approach to solve the navigation problem of a point mass in the n-dimensional space containing an arbitrary number of ellipsoidal shape obstacles. The proposed hybrid control algorithm guarantees both global asymptotic stabilization to a reference and avoidance of the obstacles. The intuitive idea of the proposed hybrid feedback is to switch between two modes of control: stabilization and avoidance. The geometric construction of the flow and jump sets of the proposed hybrid controller, exploiting hysteresis regions, guarantees Zeno-free switching between the stabilization and the avoidance modes. Simulation results illustrate the performance of the proposed hybrid control approach for 2-dimensional and 3-dimensional scenarios.

math.OC↗

arXiv2020

A hybrid barrier certificate approach to satisfy linear temporal logic specifications

In this work we formulate the satisfaction of a (syntactically co-safe) linear temporal logic specification on a physical plant through a recent hybrid dynamical systems formalism. In order to solve this problem, we introduce an extension to such a hybrid system framework of the so-called eventuality property, which matches suitably the condition for the satisfaction of such a temporal logic specification. The eventuality property can be established through barrier certificates, which we derive for the considered hybrid system framework. Using a hybrid barrier certificate, we propose a solution to the original problem. Simulations illustrate the effectiveness of the proposed method.

eess.SY↗

arXiv2020

Satisfaction of linear temporal logic specifications through recurrence tools for hybrid systems

In this work we formulate the problem of satisfying a linear temporal logic formula on a linear plant with output feedback, through a recent hybrid systems formalism. We relate this problem to the notion of recurrence introduced for the considered formalism, and we then extend Lyapunov-like conditions for recurrence of an open, unbounded set. One of the proposed relaxed conditions allows certifying recurrence of a suitable set, and this guarantees that the high-level evolution of the plant satisfies the formula, without relying on discretizations of the plant. Simulations illustrate the proposed approach.

eess.SY↗

arXiv2020

Controller design for robust invariance from noisy data

For an unknown linear system, starting from noisy open-loop input-state data collected during a finite-length experiment, we directly design a linear feedback controller that guarantees robust invariance of a given polyhedral set of the state in the presence of disturbances. The main result is a necessary and sufficient condition for the existence of such a controller, and amounts to the solution of a linear program. The benefits of large and rich data sets for the solution of the problem are discussed. A numerical example about a simplified platoon of two vehicles illustrates the method.

eess.SY↗

arXiv2020

Data-based stabilization of unknown bilinear systems with guaranteed basin of attraction

Motivated by the goal of having a building block in the direct design of data-driven controllers for nonlinear systems, we show how, for an unknown discrete-time bilinear system, the data collected in an offline open-loop experiment enable us to design a feedback controller and provide a guaranteed under-approximation of its basin of attraction. Both can be obtained by solving a linear matrix inequality for a fixed scalar parameter, and possibly iterating on different values of that parameter. The results of this data-based approach are compared with the ideal case when the model is known perfectly.

eess.SY↗

arXiv2019

Data-based guarantees of set invariance properties

For a discrete-time linear system, we use data from a single open-loop experiment to design directly a feedback controller enforcing that a given (polyhedral) set of the state is invariant and given (polyhedral) constraints on the control are satisfied. By building on classical results from model-based set invariance and a fundamental result from Willems et al., the controller designed from data has the following desirable features. The satisfaction of the above properties is guaranteed only from data, it can be assessed by solving a numerically-efficient linear program, and, under a certain rank condition, a data-based solution is feasible if and only if a model-based solution is feasible.

eess.SY↗

arXiv2019

A Hybrid Controller for Obstacle Avoidance in an n-dimensional Euclidean Space

For a vehicle moving in an $n$-dimensional Euclidean space, we present a construction of a hybrid feedback that guarantees both global asymptotic stabilization of a reference position and avoidance of an obstacle corresponding to a bounded spherical region. The proposed hybrid control algorithm switches between two modes of operation: stabilization (motion-to-goal) and avoidance (boundary-following). The geometric construction of the flow and jump sets of the hybrid controller, exploiting a hysteresis region, guarantees robust switching (chattering-free) between the stabilization and avoidance modes. Simulation results illustrate the performance of the proposed hybrid control approach for a 3-dimensional scenario.

eess.SY↗