arXiv subjects

Claudio De Persis

Publications and source records attributed to Claudio De Persis.

At least 37 records · Page 2Linked to original sources

arXiv2022

Event-triggered Control From Data

We present a data-based approach to design event-triggered state-feedback controllers for unknown continuous-time linear systems affected by disturbances. By an event, we mean state measurements transmission from the sensors to the controller over a digital network. By exploiting a sufficiently rich finite set of noisy state measurements and inputs collected off-line, we first design a data-driven state-feedback controller to ensure an input-to-state stability property for the closed-loop system ignoring the network. We then take into account sampling induced by the network and we present robust data-driven triggering strategies to (approximately) preserve this stability property. The approach is general in the sense that it allows deriving data-based versions of various popular triggering rules of the literature. In all cases, the designed transmission policies ensure the existence of a (global) strictly positive minimum inter-event times thereby excluding Zeno phenomenon despite disturbances. These results can be viewed as a step towards plug-and-play control for networked control systems, i.e., mechanisms that automatically learn to control and to communicate over a network.

eess.SY↗

arXiv2022

Learning Controllers from Data via Approximate Nonlinearity Cancellation

We introduce a method to deal with the data-driven control design of nonlinear systems. We derive conditions to design controllers via (approximate) nonlinearity cancellation. These conditions take the compact form of data-dependent semi-definite programs. The method returns controllers that can be certified to stabilize the system even when data are perturbed and disturbances affect the dynamics of the system during the execution of the control task, in which case an estimate of the robustly positively invariant set is provided.

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

Direct data-driven model-reference control with Lyapunov stability guarantees

In this work, we introduce a novel data-driven model-reference control design approach for unknown linear systems with fully measurable state. The proposed control action is composed by a static feedback term and a reference tracking block, which are shaped from data to reproduce the desired behavior in closed-loop. By focusing on the case where the reference model and the plant share the same order, we propose an optimal design procedure with Lyapunov stability guarantees, tailored to handle state measurements with additive noise. Two simulation examples are finally illustrated to show the potential of the proposed strategy as compared to the state of the art approaches.

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

On the Certainty-Equivalence Approach to Direct Data-Driven LQR Design

The linear quadratic regulator (LQR) problem is a cornerstone of automatic control, and it has been widely studied in the data-driven setting. The various data-driven approaches can be classified as indirect (i.e., based on an identified model) versus direct or as robust (i.e., taking uncertainty into account) versus certainty-equivalence. Here we show how to bridge these different formulations and propose a novel, direct, and regularized formulation. We start from indirect certainty-equivalence LQR, i.e., least-square identification of state-space matrices followed by a nominal model-based design, formalized as a bi-level program. We show how to transform this problem into a single-level, regularized, and direct data-driven control formulation, where the regularizer accounts for the least-square data fitting criterion. For this novel formulation we carry out a robustness and performance analysis in presence of noisy data. Our proposed direct and regularized formulation is also amenable to be further blended with a robust-stability-promoting regularizer. In a numerical case study we compare regularizers promoting either robustness or certainty-equivalence, and we demonstrate the remarkable performance when blending both of them.

math.OC↗

arXiv2021

Online learning of data-driven controllers for unknown switched linear systems

Motivated by the goal of learning controllers for complex systems whose dynamics change over time, we consider the problem of designing control laws for systems that switch among a finite set of unknown discrete-time linear subsystems under unknown switching signals. To this end, we propose a method that uses data to directly design a control mechanism without any explicit identification step. Our approach is online, meaning that the data are collected over time while the system is evolving in closed-loop, and are directly used to iteratively update the controller. A major benefit of the proposed online implementation is therefore the ability of the controller to automatically adjust to changes in the operating mode of the system. We show that the proposed control mechanism guarantees stability of the closed-loop switched linear system provided that the switching is slow enough. Effectiveness of the proposed design technique is illustrated for two aerospace applications.

eess.SY↗

arXiv2021

Designing Experiments for Data-Driven Control of Nonlinear Systems

In a recent paper we have shown that data collected from linear systems excited by persistently exciting inputs during low-complexity experiments, can be used to design state- and output-feedback controllers, including optimal Linear Quadratic Regulators (LQR), by solving linear matrix inequalities (LMI) and semidefinite programs. We have also shown how to stabilize in the first approximation unknown nonlinear systems using data. In contrast to the case of linear systems, however, in the case of nonlinear systems the conditions for learning a controller directly from data may not be fulfilled even when the data are collected in experiments performed using persistently exciting inputs. In this paper we show how to design experiments that lead to the fulfilment of these conditions.

eess.SY↗

arXiv2021

On data-driven stabilization of systems with quadratic nonlinearities

In this paper, we directly design a state feedback controller that stabilizes a class of uncertain nonlinear systems solely based on input-state data collected from a finite-length experiment. Necessary and sufficient conditions are derived to guarantee that the system is absolutely stabilizable and a controller is designed. Results derived under some relaxed prior information about the system and strengthened data assumptions are also discussed. Numerical examples illustrate the method with different levels of prior information.

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↗

arXiv2020

DC power grids with constant-power loads -- Part I: A full characterization of power flow feasibility, long-term voltage stability and their correspondence

In this two-part paper we develop a unifying framework for the analysis of the feasibility of the power flow equations for DC power grids with constant-power loads. In Part I of this paper we present a detailed introduction to the problem of power flow feasibility of such power grids, and the associated problem of selecting a desirable operating point which satisfies the power flow equations. We introduce and identify all long-term voltage semi-stable operating points, and show that there exists a one-to-one correspondence between such operating points and the constant power demands for which the power flow equations are feasible. Such operating points can be found by solving an initial value problem, and a parametrization of these operating points is also obtained. In addition, we give a full characterization of the set of all feasible power demands, and give a novel proof for the convexity of this set. Moreover, we present a necessary and sufficient LMI condition for the feasibility of a vector of power demands under small perturbation, which extends a necessary condition in the literature.

eess.SY↗

arXiv2020

DC power grids with constant-power loads -- Part II: nonnegative power demands, conditions for feasibility, and high-voltage solutions

In this two-part paper we develop a unifying framework for the analysis of the feasibility of the power flow equations for DC power grids with constant-power loads. Part II of this paper explores further implications of the results in Part I. In particular, we refine several results in Part I to obtain a necessary and sufficient condition for the feasibility of nonnegative power demands, which is cheaper to compute than the necessary and sufficient LMI condition in Part I. Moreover, we prove two novel sufficient conditions, which generalize known sufficient conditions for power flow feasibility in the literature. In addition, we prove that the unique long-term voltage semi-stable operating point associated to a feasible vector of power demands is a strict high-voltage solution. A parametrization of such operating points, which is dual to the parametrization in Part I, is also obtained, along with a parametrization of the boundary of the set of feasible power demands.

math.OC↗

arXiv2020

Data-driven stabilization of nonlinear polynomial systems with noisy data

In a recent paper we have shown how to learn controllers for unknown linear systems using finite-sized noisy data by solving linear matrix inequalities. In this note we extend this approach to deal with unknown nonlinear polynomial systems by formulating stability certificates in the form of data-dependent sum of squares programs, whose solution directly provides a stabilizing controller and a Lyapunov function. We then derive variations of this result that lead to more advantageous controller designs. The results also reveal connections to the problem of designing a controller starting from a least-square estimate of the polynomial system.

math.OC↗

arXiv2020

Learning control for polynomial systems using sum of squares relaxations

This paper considers the problem of learning control laws for nonlinear polynomial systems directly from the data, which are input-output measurements collected in an experiment over a finite time period. Without explicitly identifying the system dynamics, stabilizing laws are directly designed for nonlinear polynomial systems using experimental data alone. By using data-based sum of square programming, the stabilizing state-dependent control gains can be constructed.

eess.SY↗

arXiv2020

Data-driven Linear Quadratic Regulation via Semidefinite Programming

This paper studies the finite-horizon linear quadratic regulation problem where the dynamics of the system are assumed to be unknown and the state is accessible. Information on the system is given by a finite set of input-state data, where the input injected in the system is persistently exciting of a sufficiently high order. Using data, the optimal control law is then obtained as the solution of a suitable semidefinite program. The effectiveness of the approach is illustrated via numerical examples.

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

Willems' Fundamental Lemma for State-space Systems and its Extension to Multiple Datasets

Willems et al.'s fundamental lemma asserts that all trajectories of a linear system can be obtained from a single given one, assuming that a persistency of excitation condition holds. This result has profound implications for system identification and data-driven control, and has seen a revival over the last few years. The purpose of this paper is to extend Willems' lemma to the situation where multiple (possibly short) system trajectories are given instead of a single long one. To this end, we introduce a notion of collective persistency of excitation. We will then show that all trajectories of a linear system can be obtained from a given finite number of trajectories, as long as these are collectively persistently exciting. We will demonstrate that this result enables the identification of linear systems from data sets with missing data samples. Additionally, we show that the result is of practical significance in data-driven control of unstable systems.

math.OC↗