Claudio De Persis

• PhD
• Professor (Full) at University of Groningen

The paper deals with the data-based design of controllers that solve the output regulation problem for nonlinear systems. Inspired by recent developments in model-based output regulation design techniques and in data-driven control design for nonlinear systems, we derive a data-dependent semidefinite program that, when solved, directly returns a co...

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 t...

This note aims to provide a systematic understanding of direct data-driven control, enriching the existing literature not by adding another isolated result, but rather by offering a comprehensive, versatile, and unifying framework that sets the stage for future explorations and applications in this domain. To this end, we formulate the nonlinear de...

Lyapunov’s indirect method is one of the oldest and most popular approaches to model-based controller design for nonlinear systems. When the explicit model of the nonlinear system is unavailable for designing such a linear controller, finite-length off-line data is used to obtain a data-based representation of the closed-loop system, and a data-dri...

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...

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...

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 a...

We consider the feedback linearization problem, and contribute with a new method that can learn the linearizing controller from a library (a dictionary) of candidate functions. When the dynamics of the system are known, the method boils down to solving a set of linear equations. Remarkably, the same idea extends to the case in which the dynamics of...

We propose a data-driven control design method for nonlinear systems that builds on kernel-based interpolation. Under some assumptions on the system dynamics, kernel-based functions are built from data and a model of the system, along with deterministic model error bounds, is determined. Then, we derive a controller design method that aims at stabi...

For an unknown linear system, starting from noisy 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...

We present a novel framework for transferring the knowledge from one system (source) to design a stabilizing controller for a second system (target). Our motivation stems from the hypothesis that abundant data can be collected from the source system, whereas the data from the target system is scarce. We consider both cases where data collected from...

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...

In this note, we present a novel framework for transferring the knowledge from one system (source) to design a stabilizing controller for a second system (target). Our motivation stems from the hypothesis that abundant data can be collected from the source system, whereas the data from the target system is scarce. We consider both cases where data...

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 mecha...

We address the problem of designing a stabilizing closed-loop control law directly from input and state measurements collected in an experiment. In the presence of a process disturbance 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 dynamic...

For data-driven control of nonlinear systems, the basis functions characterizing the dynamics are usually essential. In existing works, the basis functions are often carefully chosen based on pre-knowledge of the dynamics so that the system can be expressed or well-approximated by the basis functions and the experimental data. For a more general se...

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...

In this paper, we investigate a networked control problem in the presence of Denial-of-Service (DoS) attacks, which prevent transmissions over the communication network. The communication between the process and controller is also subject to bit rate constraints. For mitigating the influences of DoS attacks and bit rate constraints, we develop a va...

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 s...

This paper considers the problem of Nash equilibrium (NE) seeking in aggregative games, where the cost function of each player depends on an aggregate of all players' actions. We present a distributed continuous‐time algorithm such that the actions of the players converge to NE by communicating to each other through a connected network. As agents m...

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 po...

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. We present a necessary and sufficient LMI condition for the feasibility of a vector of power demands (under...

In an 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; the corresponding state sequence (and state derivative sequence, in continuous time) is measured. The goal is to design directly from the input and state sequences a...

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 si...

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 c...

In a recent paper, we have shown how to learn controllers for unknown linear systems using finite length 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...

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 robu...

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...

This paper addresses a class of network games played by dynamic agents using their outputs. Unlike most existing related works, the Nash equilibrium in this work is defined by functions of agent outputs instead of full agent states, which allows the agents to have more general and heterogeneous dynamics and maintain some privacy of their local stat...

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, w...

The question of security is becoming central for the current generation of engineering systems which more and more rely on networks to support monitoring and control tasks. This chapter addresses the question of designing network control systems that are resilient to Denial-of-Service, that is to phenomena which render a communication network unava...

This paper considers the Linear Quadratic Regulator problem for linear systems with unknown dynamics, a central problem in data-driven control and reinforcement learning. We propose a method that uses data to directly return a controller without estimating a model of the system. Sufficient conditions are given under which this method returns a stab...

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 mecha...

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 show...

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 s...

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 th...

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, w...

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 f...

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 di...

Motivated by the goal of having a building block in the design of direct 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 underapproximation of its basin of attraction. Bot...

In this two-part paper we study the feasibility of the power flow equations of DC power grids with constant power loads. In Part I of this paper we present a rigorous introduction into the problem of power flow feasibility of such power grids, and the problem of selecting a desirable operating point which satisfies the power flow equations. Our mai...

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...

This paper considers the Linear Quadratic Regulator problem for linear systems with unknown dynamics, a central problem in data-driven control and reinforcement learning. We propose a method that uses data to directly return a controller without estimating a model of the system. Sufficient conditions are given under which this method returns a stab...

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. Bo...

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 and a controllability condition hold. This result has profound implications for system identification and data-driven control, and has seen a revival over the last few years. The p...

This paper investigates the problem of estimating biases affecting relative state measurements in a sensor network. Each sensor measures the relative states of its neighbors and this measurement is corrupted by a constant bias. We analyse under what conditions on the network topology and the maximum number of biased sensors the biases can be correc...

This paper considers the problem of learning control laws for nonlinear polynomial systems directly from 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 by solving sum of square...

We study communication-constrained networked control problems for linear time-invariant systems in the presence of Denial-of-Service (DoS) attacks, namely attacks that prevent transmissions over the communication network. Our work aims at exploring the trade-offs between system resilience and network bandwidth capacity. Given a class of DoS attacks...

In a consensus network subject to non-zero mean noise, the system state may be driven away even when the disagreement exhibits a bounded response. This is unfavourable in applications since the nodes may not work properly and even be faulty outside their operating region. In this paper, we propose a new control algorithm to mitigate this issue by a...

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...

For a discrete-time linear system, we use data from an open-loop experiment to design directly a linear 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...

In this paper we study a power grid which consists of interconnected DC microgrids. These microgrids are equipped with constant-power loads, and the lines in the grid are assumed to be purely resistive. For this setup we present a sufficient condition which ensures that the power flow equations are feasible. The novelty of this condition is its plu...

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 optima...

In a paper by Willems et al. , it was shown that persistently exciting data can be used to represent the input–output behavior of a linear system. Based on this fundamental result, we derive a parametrization of linear feedback systems that paves the way to solve important control problems using data-dependent linear matrix inequalities only. The...

Continuous-time gradient-based Nash equilibrium seeking algorithms enjoy a passivity property under a suitable monotonicity assumption, which has been exploited to design distributed Nash equilibrium seeking algorithms. We further exploit the passivity property to interconnect the algorithms with distributed nonlinear averaging integral controllers...

This paper addresses a class of network games played by dynamic agents using their outputs. Unlike most existing related works, the Nash equilibrium in this work is defined by functions of agent outputs instead of full agent states, which allows the agents to have more general and heterogeneous dynamics and maintain some privacy of their local stat...

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 W...

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 optima...

This paper considers the problem of Nash equilibrium (NE) seeking in aggregative games, where the payoff function of each player depends on an aggregate of all players' actions. We present a distributed continuous time algorithm such that the actions of the players converge to NE by communicating to each other through a connected network. A major c...

We consider continuous-time equilibrium seeking in a class of aggregative games with strongly convex cost functions and affine coupling constraints. We propose simple, semi-decentralized integral dynamics and prove their global asymptotic convergence to a variational generalized aggregative or Nash equilibrium. The proof is based on Lyapunov argume...

This paper proposes a distributed sliding mode (SM) control strategy for optimal load frequency control (OLFC) in power networks, where besides frequency regulation, minimization of generation costs is also achieved (economic dispatch). We study a nonlinear power network of interconnected (equivalent) generators, including voltage and second-order...

In this paper a novel distributed control algorithm for current sharing and voltage regulation in Direct Current (DC) microgrids is proposed. The DC microgrid is composed of several Distributed Generation units (DGUs), including Buck converters and current loads. The considered model permits an arbitrary network topology and is affected by unknown...

This paper investigates the problem of estimating biases affecting relative state measurements in a sensor network. Each sensor measures the relative states of its neighbors and this measurement is corrupted by a constant bias. We analyse under what conditions on the network topology and the maximum number of biased sensors the biases can be correc...

This paper deals with coordination problems over noisy communication channels. We consider a scenario where the communication between network nodes is corrupted by unknown-but-bounded noise. We introduce a novel coordination scheme which ensures (i) boundedness of the state trajectories, and (ii) a linear map from the noise to the nodes disagreemen...

In this paper we study the DC power flow equations of a purely resistive DC power grid which consists of interconnected DC microgrids with constant-power loads. We present a condition on the power grid which guarantees the existence of a solution to the power flow equations. In addition, we present a condition for any microgrid in island mode which...

In a paper by Willems and coworkers it was shown that sufficiently excited data could be used to represent the input-output trajectory of a linear system. Based on this fundamental result, we derive a parametrization of linear feedback systems that paves the way to solve important control problems using data-dependent Linear Matrix Inequalities onl...

This paper proposes a decentralized Second Order Sliding Mode (SOSM) control strategy for Load Frequency Control (LFC) in power networks, regulating the frequency and maintaining the net inter-area power flows at their scheduled values. The considered power network is partitioned into control areas, where each area is modelled by an equivalent gene...

Continuous-time gradient-based Nash equilibrium seeking algorithms enjoy a passivity property under a suitable monotonicity assumption. This feature has been exploited to design distributed algorithms that converge to Nash equilibria and use local information only. We further exploit the passivity property to interconnect the algorithms with distri...

We investigate the performance and robustness of distributed averaging integral controllers used in the optimal frequency regulation of power networks. We construct a strict Lyapunov function that allows us to quantify the exponential convergence rate of the closed-loop system. As an application, we study the stability of the system in the presence...

We study communication-constrained networked control problems for linear time-invariant systems in the presence of Denial-of-Service (DoS) attacks, namely attacks that prevent transmissions over the communication network. Our work aims at exploring the relationship between system resilience and network bandwidth capacity. Given a class of DoS attac...

This paper investigates coordination problems over packet-based communication channels. We consider the scenario in which the communication between network nodes is corrupted by unknown-but-bounded noise. We introduce a novel coordination scheme, which ensures practical consensus in the noiseless case, while preserving bounds on the nodes disagreem...

We investigate the robustness of distributed averaging integral controllers for optimal frequency regulation of power networks to noise in measurements, communication and actuation. Specifically, using Lyapunov techniques, we show a property related to input-to-state stability of the closed loop system with respect to this noise. Using this result,...

In this chapter, we investigate Self-Triggered synchronization of linear oscillators in the presence of communication failures caused by denial-of-Service (DoS). A general framework is considered in which network links can fail independent of each other. A characterization of DoS frequency and duration to preserve network synchronization is provide...

In this paper a novel distributed control algorithm for voltage regulation and current sharing in Direct Current (DC) microgrids is proposed. The DC microgrid is composed of several Distributed Generation units, interfaced with Buck converters, and unknown current loads. The proposed control strategy exploits a communication network to achieve curr...