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Claudio De Persis

Publications and source records attributed to Claudio De Persis.

At least 55 records · Page 3Linked to original sources
arXiv2020

Low-complexity Learning of Linear Quadratic Regulators from Noisy Data

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 stabilizing controller with guaranteed relative error when the data used to design the controller are affected by noise. This method has low complexity as it only requires a finite number of samples of the system response to a sufficiently exciting input, and can be efficiently implemented as a semi-definite program. Further, the method does not require assumptions on the noise statistics, and the relative error nicely scales with the noise magnitude.

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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.

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arXiv2019

Network games with dynamic players: Stabilization and output convergence to Nash equilibrium

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 states. The concerned network game is formulated with agents modeled by uncertain linear systems subject to external disturbances. The cost function of each agent is a linear quadratic function depending on the outputs of its own and its neighbors in the underlying graph. The main challenge stemming from this game formulation is that merely driving the agent outputs to the Nash equilibrium does not guarantee the stability of the agent dynamics. Using local output and the outputs from the neighbors of each agent, we aim at designing game strategies that achieve output Nash equilibrium seeking and stabilization of the closed-loop dynamics. Particularly, when each agents knows how the actions of its neighbors affect its cost function, a game strategy is developed for network games with digraph topology. When each agent is also allowed to exchange part of its compensator state, a distributed strategy can be designed for networks with connected undirected graphs or connected digraphs.

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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.

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arXiv2019

Privacy and Robustness Guarantees in Distributed Dynamics for Aggregative Games

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 concern in communicative schemes among strategic agents is that their private information may be revealed to other agents or to a curious third party who can eavesdrop the communications. We address this concern for the presented algorithm and show that private information of the players cannot be reconstructed even if all the communicated variables are compromised. As agents may deviate from their optimal strategies dictated by the NE seeking protocol, we investigate robustness of the proposed algorithm against time-varying disturbances. In particular, we provide rigorous robustness guarantees by proving input to state stability (ISS) properties of the NE seeking dynamics. Finally, we demonstrate practical applications of our theoretical findings on two case studies; namely, on an energy consumption game and a charging coordination problem of electric vehicles.

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arXiv2019

Formulas for Data-driven Control: Stabilization, Optimality and Robustness

In a paper by Willems and coauthors 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 result is remarkable in that no explicit system's matrices identification is required. The examples of control problems we solve include the state and output feedback stabilization, and the linear quadratic regulation problem. We also discuss robustness to noise-corrupted measurements and show how the approach can be used to stabilize unstable equilibria of nonlinear systems.

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arXiv2019

Bias estimation in sensor networks

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 correctly estimated. We show that for non-bipartite graphs the biases can always be determined even when all the sensors are corrupted, while for bipartite graphs more than half of the sensors should be unbiased to ensure the correctness of the bias estimation. If the biases are heterogeneous, then the number of unbiased sensors can be reduced to two. Based on these conditions, we propose some algorithms to estimate the biases.

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arXiv2019

Plug-and-play Solvability of the Power Flow Equations for Interconnected DC Microgrids with Constant Power Loads

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 guarantees that the power grid remains feasible upon interconnection. These conditions provide a method to determine if a power grid remains feasible after the interconnection with a specific microgrid with constant-power loads. Although the presented condition are more conservative than existing conditions in the literature, its novelty lies in its plug-and-play property. That is, the condition gives a restriction on the to-be-connected microgrid, but does not impose more restrictions on the rest of the power grid.

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arXiv2018

Distributed averaging integral Nash equilibrium seeking on networks

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 distributed averaging integral controllers that tune on-line the weights of the communication graph. The main advantage is to guarantee convergence to a Nash equilibrium without requiring a strong coupling condition on the algebraic connectivity of the communication graph over which the players exchange information, nor a global high-gain.

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arXiv2018

Robust Decentralized Secondary Frequency Control in Power Systems: Merits and Trade-Offs

Frequency restoration in power systems is conventionally performed by broadcasting a centralized signal to local controllers. As a result of the energy transition, technological advances, and the scientific interest in distributed control and optimization methods, a plethora of distributed frequency control strategies have been proposed recently that rely on communication amongst local controllers. In this paper we propose a fully decentralized leaky integral controller for frequency restoration that is derived from a classic lag element. We study steady-state, asymptotic optimality, nominal stability, input-to-state stability, noise rejection, transient performance, and robustness properties of this controller in closed loop with a nonlinear and multivariable power system model. We demonstrate that the leaky integral controller can strike an acceptable trade-off between performance and robustness as well as between asymptotic disturbance rejection and transient convergence rate by tuning its DC gain and time constant. We compare our findings to conventional decentralized integral control and distributed-averaging-based integral control in theory and simulations.

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arXiv2018

Output Impedance Diffusion into Lossy Power Lines

Output impedances are inherent elements of power sources in the electrical grids. In this paper, we give an answer to the following question: What is the effect of output impedances on the inductivity of the power network? To address this question, we propose a measure to evaluate the inductivity of a power grid, and we compute this measure for various types of output impedances. Following this computation, it turns out that network inductivity highly depends on the algebraic connectivity of the network. By exploiting the derived expressions of the proposed measure, one can tune the output impedances in order to enforce a desired level of inductivity on the power system. Furthermore, the results show that the more "connected" the network is, the more the output impedances diffuse into the network. Finally, using Kron reduction, we provide examples that demonstrate the utility and validity of the method.

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arXiv2018

Data Rates for Stabilizing Control under Denial-of-Service Attacks

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 attacks, we first characterize time-invariant bit-rate bounds that are dependent on the unstable eigenvalues of the dynamic matrix of the plant and the parameters of DoS attacks, beyond which exponential stability of the closed-loop system can be guaranteed. Second, we design the time-varying bit-rate protocol and show that it can enable the system to maintain the comparable robustness as the one under the time-invariant bit-rate protocol and meanwhile promote the possibility of transmitting fewer bits especially when the attack levels are low. Our characterization clearly shows the trade-off between the communication bandwidth and resilience against DoS. An example is given to illustrate the proposed solution approach.

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arXiv2018

Self-Triggered Network Coordination over Noisy Communication Channels

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 disagreement in the noisy case. The proposed scheme does not require any global information about the network parameters and/or the operating environment (the noise characteristics). Moreover, network nodes can sample at independent rates and in an aperiodic manner. The analysis is substantiated by extensive numerical simulations.

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arXiv2018

A Robust Consensus Algorithm for Current Sharing and Voltage Regulation in DC Microgrids

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 load demand and modelling uncertainties. The proposed control strategy exploits a communication network to achieve proportional current sharing using a consensus-like algorithm. Voltage regulation is achieved by constraining the system to a suitable manifold. Two robust control strategies of Sliding Mode (SM) type are developed to reach the desired manifold in a finite time. The proposed control scheme is formally analyzed, proving the achievement of proportional current sharing, while guaranteeing that the weighted average voltage of the microgrid is identical to the weighted average of the voltage references.

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arXiv2018

Continuous-time integral dynamics for Aggregative Game equilibrium seeking

In this paper, we consider continuous-time semi-decentralized dynamics for the equilibrium computation in a class of aggregative games. Specifically, we propose a scheme where decentralized projected-gradient dynamics are driven by an integral control law. To prove global exponential convergence of the proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov function argument. We derive a sufficient condition for global convergence that we position within the recent literature on aggregative games, and in particular we show that it improves on established results.

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arXiv2018

Hybrid interconnection of iterative bidding and power network dynamics for frequency regulation and optimal dispatch

This paper considers a real-time electricity market involving an independent system operator (ISO) and a group of strategic generators. The ISO operates a market where generators bid prices at which there are willing to provide power. The ISO makes power generation assignments with the goal of solving the economic dispatch problem and regulating the network frequency. We propose a multi-rate hybrid algorithm for bidding and market clearing that combines the discrete nature of iterative bidding with the continuous nature of the frequency evolution in the power network. We establish sufficient upper bounds on the inter-event times that guarantee that the proposed algorithm asymptotically converges to an equilibrium corresponding to an efficient Nash equilibrium and zero frequency deviation. Our technical analysis builds on the characterization of the robustness properties of the continuous-time version of the bidding update process interconnected with the power network dynamics via the identification of a novel LISS-Lyapunov function. Simulations on the IEEE 14-bus system illustrate our results.

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arXiv2018

A feedback control algorithm to steer networks to a Cournot-Nash equilibrium

We propose a distributed feedback control that steers a dynamical network to a prescribed equilibrium corresponding to the so-called Cournot-Nash equilibrium. The network dynamics considered here are a class of passive nonlinear second-order systems, where production and demands act as external inputs to the systems. While productions are assumed to be controllable at each node, the demand is determined as a function of local prices according to the utility of the consumers. Using reduced information on the demand, the proposed controller guarantees the convergence of the closed loop system to the optimal equilibrium point dictated by the Cournot-Nash competition.

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