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This paper proposes a model reduction approach for simplifying the interconnection topology of Lur'e network systems. A class of reduced-order models are generated by the projection framework based on graph clustering, which not only preserve the network structure but also ensure absolute stability. Furthermore, we provide an upper bound on the input-output approximation error between the original and reduced-order Lur'e network systems, which is expressed as a function of the characteristic matrix of graph clustering. Finally, the results are illustrated via a numerical example., Comment: to appear in 22nd European Control Conference (ECC24), Stockholm, Sweden

In this paper, we consider the problem of voltage stability in DC networks containing uncertain loads with non-monotone incremental impedances and where the steady-state power availability is restricted to a subset of the buses in the network. We propose controllers for powered buses that guarantee voltage regulation and output strictly equilibrium independent passivity (OS-EIP) of the controlled buses, while buses without power are equipped with controllers that dampen their transient behaviour. The OS-EIP of a cluster containing both bus types is verified through a linear matrix inequality (LMI) condition, and the asymptotic stability of the overall microgrid with uncertain, non-monotone loads is ensured by interconnecting the OS-EIP clusters. By further employing singular perturbation theory, we show that the OS-EIP property of the clusters is robust against certain network parameter and topology changes.

Demand response has been a promising solution for accommodating renewable energy in power systems. In this study, we consider a demand response scheme within a distribution network facing an energy supply deficit. The utility company incentivizes load aggregators to adjust their pre-scheduled energy consumption and generation to match the supply. Each aggregator, which represents a group of prosumers, aims to maximize its revenue by bidding strategically in the demand response scheme. Since aggregators act in their own self-interest and their revenues and feasible bids influence one another, we model their competition as a network-constrained aggregative game. This model incorporates power flow constraints to prevent potential line congestion. Given that there are no coordinators and aggregators can only communicate with their neighbours, we introduce a fully distributed generalized Nash equilibrium seeking algorithm to determine the optimal bidding strategies for aggregators in this game. Within this algorithm, only estimates of the aggregate and certain auxiliary variables are communicated among neighbouring aggregators. We demonstrate the convergence of this algorithm by constructing an equivalent iteration using the forward-backward splitting technique.

This paper addresses the trajectory-tracking problem for a class of electromechanical systems. To this end, the dynamics of the plants are modeled in the so-called port-Hamiltonian framework. Then, the notion of contraction is exploited to design the desired closed-loop dynamics and the corresponding tracking controller. Notably, the proposed control design method does not require solving partial differential equations or changing the coordinates of the plant, which permits preserving the physical interpretation of the controller. The applicability of the proposed approach is illustrated in several electromechanical systems via simulations.

This paper presents a new modelling approach to fully dynamic electromagnetic current-controlled piezoelectric composite models that require a combined Lagrangian. To model the mechanical domains, we consider two different beam theories, i.e. the Euler-Bernoulli and Timoshenko beam theories. We show that both derived piezoelectric composite models are well-posed. Furthermore, we show through analysis and simulations that both current-controlled piezoelectric composites are asymptotically stabilizable through simple electric feedback, which renders the system passive in a classical way for certain system parameters. In this work, we also review several related piezoelectric beams, actuators, and composite models., Comment: 18 pages, 3 figures, 2 tables. This work is intended to be submitted for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. arXiv admin note: text overlap with arXiv:2309.00947

In this paper, we present a new piezoelectric actuator and piezoelectric composite model and show the well-posedness of these systems. Furthermore, we show that the piezoelectric composite is stabilizable for certain system parameters. In this work, we also review several piezoelectric beams, actuators, and composite models and provide improved definitions of the different electromagnetic considerations, i.e. fully dynamic electromagnetic field, quasi-static electric field, and the static lectric field assumption., Comment: 19 pages, 5 figures, 2 tables. This work is intended to be submitted for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

Securely and efficiently procuring energy balancing services in distribution networks remains challenging, especially within a privacy-preserving environment. This paper proposes a network-constrained demand response game, i.e., a Generalized Nash Game (GNG), to incentivize energy consumers to offer balancing services. Specifically, we adopt a supply function-based bidding method for our demand response problem, where a requisite load adjustment must be met. To ensure the secure operation of distribution networks, we incorporate physical network constraints, including line capacity and bus voltage limits, into the game formulation. In addition, we analytically evaluate the efficiency loss of this game. Previous approaches to steer energy consumers toward the Generalized Nash Equilibrium (GNE) of the game often necessitated sharing some private information, which might not be practically feasible or desired. To overcome this limitation, we propose a decentralized market clearing algorithm with analytical convergence guarantees, which only requires the participants to share limited, non-sensitive information with others. Numerical analyses illustrate that the proposed market mechanism exhibits a low market efficiency loss. Moreover, these analyses highlight the critical role of integrating physical network constraints. Finally, we demonstrate the scalability of our proposed algorithm by conducting simulations on the IEEE 33-bus and 69-bus test systems.

A fundamental precondition for the secure and efficient operation of district heating networks (DHNs) is a stable hydraulic behavior. However, the ongoing transition towards a sustainable heat supply, especially the rising integration of distributed heat sources and the increasingly meshed topologies, introduce complex and potentially destabilizing hydraulic dynamics. In this work, we propose a unifying, passivity-based framework which guarantees asymptotic stability of any forced hydraulic DHN equilibrium while allowing for meshed, time-varying topologies and different, dynamically interacting distributed heat sources. To establish the desired hydraulic equilibria, we propose decentralized, passivity-based pressure and volume flow rate controllers for the pumps and valves in the actuated DHN subsystems. In particular, we leverage the equilibrium-independent passivity (EIP) properties of the DHN subsystems, the skew-symmetric nature of their interconnections, and LaSalle's Invariance principle to assess asymptotic stability in a modular manner. The obtained results hold for the state-of-the-art as well as future DHN generations featuring, for example, multiple distributed heat sources, asymmetric pipe networks, and multiple temperature layers. We verify our findings by means of simulations.

This paper proposes a port-Hamiltonian framework for angle-based formation stabilization and maneuvers using bearing and velocity measurements with an underlying triangulated Laman graph. The corresponding port-Hamiltonian controller is designed using virtual couplings on the errors of angle constraints in angle space and then the angle constraints and agent actuators are mapped by the constraint Jacobian, which can be applied to other formation constraints. In addition, due to the fact that the port-Hamiltonian model allows for complex and heterogeneous agent dynamics, our framework can be extended to networks with different agent dynamics and formation constraints. To avoid unavailable distance terms in the control law, an estimator is designed based on port-Hamiltonian theory and the property that energy is coordinate-free for different sensor modalities using bearing and velocity measurements, which permits our framework to inject damping for the formation maneuvers. Furthermore, several maneuvers are analyzed under both considerations of stabilization and transient performance. Simulations are performed to illustrate the effectiveness of the approach.

This paper proposes a passivity-based port-Hamiltonian (pH) framework for multi-agent displacement-based and rigid formation control and velocity tracking. The control law consists of two parts, where the internal feedback is to track the velocity and the external feedback is to achieve formation stabilization by steering variables of neighboring agents that prescribe the desired geometric shape. Regarding the external feedback, a general framework is proposed for all kinds of formations by means of the advantage that the pH model is energy-based and coordinate-free. To solve the issue that the incidence matrix is not of full column rank over cyclic graphs, the matrix property is used to prove the convergence to the target sets for the displacement-based formation, while for rigid formations, the algebraic conditions of infinitesimal rigidity are investigated to achieve asymptotic local stability. Furthermore, the rigid formation with heterogeneous constraints is further investigated under this framework and the asymptotic local stability is proved under a mild assumption. Simulations are performed to illustrate the effectiveness of the framework.

This manuscript introduces a passivity-based control methodology for fully-actuated mechanical systems with symmetric or asymmetric dead-zones. To this end, we find a smooth approximation of the inverse of the function that describes such a nonlinearity. Then, we propose an energy and damping injection approach - based on the PI-PBC technique - that compensates for the dead-zone. Moreover, we provide an analysis of the performance of the proposed controller near the equilibrium. We conclude this paper by experimentally validating the results on a two degrees-of-freedom planar manipulator., Comment: Accepted in NOLCOS 2022

Motivated by current sharing in power networks, we consider a class of output consensus (also called agreement) problems for nonlinear systems, where the consensus value is determined by external disturbances, e.g., power demand. This output consensus problem is solved by a simple distributed output feedback controller if a system is either Krasovskii or shifted passive, which is the only essential requirement. The effectiveness of the proposed controller is shown in simulation on an islanded DC power network.

Modern district heating technologies have a great potential to make the energy sector more flexible and sustainable due to their capabilities to use energy sources of varied nature and to efficiently store energy for subsequent use. Central control tasks within these systems for the efficient and safe distribution of heat refer to the stabilization of overall system temperatures and the regulation of storage units state of charge. These are challenging goals when the networked and nonlinear nature of district heating system models is taken into consideration. In this letter, for district heating systems with multiple, distributed heat producers, we propose a decentralized control scheme to provably meet said tasks stably.

This paper addresses the aggregated monitoring problem for large-scale network systems with a few dedicated sensors. Full state estimation of such systems is often infeasible due to unobservability and/or computational infeasibility. Therefore, through clustering and aggregation, a tractable representation of a network system, called a projected network system, is obtained for designing a minimum-order average state observer. This observer estimates the average states of the clusters, which are identified with explicit consideration to the estimation error. Moreover, given the clustering, the proposed observer design algorithm exploits the structure of the estimation error dynamics to achieve computational tractability. Simulations show that the computation of the proposed algorithm is significantly faster than the usual $\mathcal{H}_2/\mathcal{H}_\infty$ observer design techniques. On the other hand, compromise on the estimation error characteristics is shown to be marginal.

In this paper we propose an original distributed control framework for DC mcirogrids. We first formulate the (optimal) control objectives as an aggregative game suitable for the energy trading market. Then, based on the dual theory, we analyze the equivalent distributed optimal condition for the proposed aggregative game and design a distributed control scheme to solve it. By interconnecting the DC mcirogrid and the designed distributed control system in a power preserving way, we steer the DC microgrid's state to the desired optimal equilibrium, satisfying a predefined set of local and coupling constraints. Finally, based on the singular perturbation system theory, we analyze the convergence of the closed-loop system. The simulation results show excellent performance of the proposed control framework.

This manuscript introduces a passivity-based integral control approach for fully-actuated mechanical systems. The novelty of our methodology is that we exploit the gyroscopic forces of the mechanical systems to exponentially stabilize the mechanical system at the desired equilibrium even in the presence of matched disturbances; additionally, we show that our approach is robust against unmatched disturbances. Furthermore, we provide tuning rules to prescribe the performance of the closed-loop system. We conclude this manuscript with experimental results obtained from a robotic arm., Comment: Draft for CDC 2022

This manuscript describes several approaches to tune the parameters of a class of passivity-based controllers for standard nonlinear mechanical systems. In particular, we are interested in controllers that preserve the mechanical system structure in closed-loop. To this end, first, we provide tuning rules for stabilization, i.e., the rate of convergence (exponential stability) and stability margin (input-to-state stability). Then, we provide guidelines to remove the overshoot while prescribing the rise time. Additionally, we propose a methodology to tune the gyroscopic-related parameters. We also provide remarks on the damping phenomena to facilitate the practical implementation of our approaches. We conclude this paper with experimental results obtained from applying our tuning rules to an underactuated and a fully-actuated mechanical configuration.

This paper proposes a data-driven model reduction approach on the basis of noisy data. Firstly, the concept of data reduction is introduced. In particular, we show that the set of reduced-order models obtained by applying a Petrov-Galerkin projection to all systems explaining the data characterized in a large-dimensional quadratic matrix inequality (QMI) can again be characterized in a lower-dimensional QMI. Next, we develop a data-driven generalized balanced truncation method that relies on two steps. First, we provide necessary and sufficient conditions such that systems explaining the data have common generalized Gramians. Second, these common generalized Gramians are used to construct projection matrices that allow to characterize a class of reduced-order models via generalized balanced truncation in terms of a lower-dimensional QMI by applying the data reductionconcept. Additionally, we present alternative procedures to compute a priori and a posteriori upper bounds with respect to the true system generating the data. Finally, the proposed techniques are illustrated by means of application to an example of a system of a cart with a double-pendulum., Comment: 14 pages, 5 figures

This paper provides a constructive passivity-based control approach to solve the set-point regulation problem for input-affine continuous nonlinear systems while considering saturation in the inputs. As customarily in passivity-based control, the methodology consists of two steps: energy shaping and damping injection. In terms of applicability, the proposed controllers have two advantages concerning other passivity-based control techniques: (i) the energy shaping is carried out without solving partial differential equations, and (ii) the damping injection is performed without measuring the passive output. The proposed methodology is suitable to control a broad range of physical systems, e.g., mechanical, electrical, and electro-mechanical systems. We illustrate the applicability of the technique by designing controllers for systems in different physical domains, where we validate the analytical results via simulations and experiments., Comment: 38 pages, 11 figures, 5 tables

This paper proposes a Real-Time Market (RTM) platform for an aggregator and its corresponding prosumers to participate in the electricity wholesale market. The proposed energy market platform is modeled as a bilevel optimization problem where the aggregator and the prosumers are considered as self-interest agents. The current state-of-the-art Mathematical Programming with Equilibrium Constraints (MPEC) and Mixed-Integer Programming (MIP) based approaches to solve bilevel optimization problems are not satisfactory for real-time applications. The computation time for such approaches grows exponentially as the number of prosumers and decision variables increase. This paper presents a convex optimization problem which can capture a subset of the set of global optima of the bilevel problem as its optimal solution.

This paper provides an $H_2$ optimal scheme for reducing diffusively coupled second-order systems evolving over undirected networks. The aim is to find a reduced-order model that not only approximates the input-output mapping of the original system but also preserves crucial structures, such as the second-order form, asymptotically stability, and diffusive couplings. To this end, an $H_2$ optimal approach based on a convex relaxation is implemented to reduce the dimension, yielding a lower order asymptotically stable approximation of the original second-order network system. Then, a novel graph reconstruction approach is employed to convert the obtained model to a reduced system that is interpretable as an undirected diffusively coupled network. Finally, the effectiveness of the proposed method is illustrated via a large-scale networked mass-spring-damper system.

Flow and storage volume regulation is essential for the adequate transport and management of energy resources in district heating systems. In this letter, we propose a novel and suitably tailored -- decentralized -- adaptive control scheme addressing this problem whilst offering closed-loop stability guarantees. We focus on a system configuration comprising multiple heat producers, consumers and storage tanks exchanging energy through a common distribution network, which are features of modern and prospective district heating installations. {\color{black}The proposed controller is based on passivity, backstepping and (indirect) adaptive control theory.

Motivated by the inadequacy of conventional control methods for power networks with a large share of renewable generation, in this paper we study the (stochastic) passivity property of wind turbines based on the Doubly Fed Induction Generator (DFIG). Differently from the majority of the results in the literature, where renewable generation is ignored or assumed to be constant, we model wind power generation as a stochastic process, where wind speed is described by a class of stochastic differential equations. Then, we design a distributed control scheme that achieves load frequency control and economic dispatch, ensuring the stochastic stability of the controlled network., Comment: arXiv admin note: text overlap with arXiv:2010.12840

In this paper, we study how to alleviate highway traffic congestions by encouraging plug-in electric and hybrid vehicles to stop at charging stations around peak congestion times. Specifically, we focus on a case study and simulate the adoption of a dynamic charging price depending on the traffic congestion. We use real traffic data of the A13 highway stretch between The Hague and Rotterdam, in The Netherlands, to identify the Cell Transmission Model. Then, we apply the algorithm proposed in (Part I: Theory) to different scenarios, validating the theoretical results and showing the benefits of our strategy in terms of traffic congestion alleviation. Finally, we carry out a sensitivity analysis of the proposed algorithm and discuss how to optimize its performance., Comment: 10 pages, 14 figures, 3 tables

In this paper, we study how to alleviate highway traffic congestion by encouraging plug-in hybrid and electric vehicles to stop at a charging station around peak congestion times. Specifically, we design a pricing policy to make the charging price dynamic and dependent on the traffic congestion, predicted via the cell transmission model, and the availability of charging spots. Furthermore, we develop a novel framework to model how this policy affects the drivers' decisions by formulating a mixed-integer potential game. Technically, we introduce the concept of "road-to-station" (r2s) and "station-to-road" (s2r) flows, and show that the selfish actions of the drivers converge to charging schedules that are individually optimal in the sense of Nash. In the second part of this work, submitted as a separate paper (Part II: Case Study), we validate the proposed strategy on a simulated highway stretch between The Hague and Rotterdam, in The Netherlands., Comment: 10 pages, 2 figures

Large-scale network systems describe a wide class of complex dynamical systems composed of many interacting subsystems. A large number of subsystems and their high-dimensional dynamics often result in highly complex topology and dynamics, which pose challenges to network management and operation. This chapter provides an overview of reduced-order modeling techniques that are developed recently for simplifying complex dynamical networks. In the first part, clustering-based approaches are reviewed, which aim to reduce the network scale, i.e., find a simplified network with a fewer number of nodes. The second part presents structure-preserving methods based on generalized balanced truncation, which can reduce the dynamics of each subsystem., Comment: Chapter 11 in the book Model Order Reduction: Volume 3 Applications

Network systems consist of subsystems and their interconnections, and provide a powerful framework for analysis, modeling and control of complex systems. However, subsystems may have high-dimensional dynamics, and the amount and nature of interconnections may also be of high complexity. Therefore, it is relevant to study reduction methods for network systems. An overview on reduction methods for both the topological (interconnection) structure of the network and the dynamics of the nodes, while preserving structural properties of the network, and taking a control systems perspective, is provided. First topological complexity reduction methods based on graph clustering and aggregation are reviewed, producing a reduced-order network model. Second, reduction of the nodal dynamics is considered by using extensions of classical methods, while preserving the stability and synchronization properties. Finally, a structure-preserving generalized balancing method for simplifying simultaneously the topological structure and the order of the nodal dynamics is treated., Comment: To be published in Annual Review of Control, Robotics, and Autonomous Systems

In this paper, we prove the exponential stability property of a class of mechanical systems represented in the port-Hamiltonian framework. To this end, we propose a Lyapunov candidate function different from the Hamiltonian of the system. Moreover, we study how the proposed analysis can be used to determine the exponential stability and the rate of convergence of some (nonlinear)-mechanical systems stabilized by two passivity-based control techniques, namely, PID passivity-based control and interconnection and damping assignment. We implement the former control approach to stabilize a three degrees-of-freedom robotic arm at the desired equilibrium point to illustrate the mentioned analysis., Comment: ECC 2021- Accepted version with minor changes. Fixed a minor gramatic typo in experiments section

A new method for data-driven interpolatory model reduction is presented in this paper. Using the so-called data informativity perspective, we define a framework that enables the computation of moments at given (possibly complex) interpolation points based on time-domain input-output data only, without explicitly identifying the high-order system. Instead, by characterizing the set of all systems explaining the data, necessary and sufficient conditions are provided under which all systems in this set share the same moment at a given interpolation point. Moreover, these conditions allow for explicitly computing these moments. Reduced-order models are then derived by employing a variation of the classical rational interpolation method. The condition to enforce moment matching model reduction with prescribed poles is also discussed as a means to obtain stable reduced-order models. An example of an electrical circuit illustrates this framework., Comment: 11 pages

Motivated by the inadequacy of the existing control strategies for power systems affected by time-varying uncontrolled power injections such as loads and the increasingly widespread renewable energy sources, this paper proposes two control schemes based on the well-known output regulation control methodology. The first one is designed based on the classical output regulation theory and addresses the so-called Load Frequency Control (LFC) problem in presence of time-varying uncontrolled power injections. Then, in order to also minimize the generation costs, we use an approximate output regulation method that solves numerically only the partial differential equation of the regulator equation and propose a controller based on this solution, minimizing an appropriate penalty function. An extensive case study shows excellent performance of the proposed control schemes in different and critical scenarios.

In this paper we present new (stochastic) passivity properties for Direct Current (DC) power networks, where the unknown and unpredictable load demand is modelled by a stochastic process. More precisely, the considered power network consists of distributed generation units supplying ZIP loads, i.e., nonlinear loads comprised of impedance (Z), current (I) and power (P) components. Differently from the majority of the results in the literature, where each of these components is assumed to be constant, we consider time-varying loads whose dynamics are described by a class of stochastic differential equations. Finally, we prove that an existing distributed control scheme achieving current sharing and (average) voltage regulation ensures the asymptotic stochastic stability of the controlled network.

In this work, we propose a passivity-based control approach that addresses the trajectory tracking problem for a class of mechanical systems that comprises a broad range of robotic arms. The resulting controllers can be naturally saturated and do not require velocity measurements. Moreover, the proposed methodology does not require the implementation of observers, and the structure of the closed-loop system permits the identification of a Lyapunov function, which eases the convergence analysis. To corroborate the effectiveness of the methodology, we perform experiments with the Philips Experimental Robot Arm., Comment: 16 pages, 5 figures. It will be submitted to the European Control Conference 2021

In this paper, we propose several rules to tune the gains for a class of passivity-based controllers for nonlinear mechanical systems. Such tuning rules prescribe a desired local transient response behavior to the closed-loop system. To establish the tuning rules, we implement a PID passivity-based controller. Then, we linearize the closed-loop system, and we transform the matrix of the resulting system into a class of saddle point matrices to analyze the influence of the control gains, in terms of the oscillations and the rise time, on the transient response of the closed-loop system. Hence, the resulting controllers stabilize the plant and simultaneously address the performance of the closed-loop system. Moreover, our analysis provides a clear insight into how the kinetic energy, the potential energy, and the damping of the mechanical system are related to its transient response, endowing in this way the tuning rules with a physical interpretation. Additionally, we corroborate the analytical results through the practical implementation of a controller that stabilizes a two degrees-of-freedom (DoF) planar manipulator, where the control gains are tuned following the proposed rules., Comment: Final submission for journal: IEEE Control Systems Letters

In this paper we propose a novel current actuated fully dynamic piezoelectric composite model. This new model complements the existing modeling framework of deriving piezoelectric models. We show that the novel composite model is well-posed. Furthermore, we consider two approximation methods, FEM and MFEM and investigate the stabilizability properties. Finally, we include the closed-loop behaviour in the numerical results., Comment: This work is intended to be submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

A method for data-driven interpolatory model reduction is presented in this extended abstract. This framework enables the computation of the transfer function values at given interpolation points based on time-domain input-output data only, without explicitly identifying the high-order system. Instead, by characterizing the set of all systems explaining the data, necessary and sufficient conditions are given under which all systems in this set share the same transfer function value at a given interpolation point. After following this so-called data informativity perspective, reduced-order models can be obtained by classical interpolation techniques. An example of an electrical circuit illustrates this framework., Comment: 4 pages, 1 figure, This work is accepted as a Late-Breaking result at the IFAC World Congress 2020

In this extended abstract, we propose a tuning approach for nonlinear mechanical systems to modify the behavior of the closed-loop system, where we are particularly interested in attenuating oscillations from the transient response. Towards this end, we inject damping into the system, and we provide two tuning methods to select the gains that are appropriate for our purposes. Furthermore, we apply these tuning rules to a 2DoF planar manipulator and present its simulation results., Comment: This work is accepted as a Late-Breaking result at the IFAC World Congress 2020 Version 2 changes: -Corrected minor typos -Corrected equation 21 and 27

This paper studies the static economic optimization problem of a system with a single aggregator and multiple prosumers in a Real-Time Balancing Market (RTBM). The aggregator, as the agent responsible for portfolio balancing, needs to minimize the cost for imbalance satisfaction in real-time by proposing a set of optimal personalized prices to the prosumers. On the other hand, the prosumers, as price taker and self-interested agents, want to maximize their profit by changing their supplies or demands and providing flexibility based on the proposed personalized prices. We model this problem as a bilevel optimization problem. We first show that the optimal solution of this bilevel optimization problem can be found by solving an equivalent convex problem. In contrast to the state-of-the-art Mixed-Integer Programming (MIP)-based approach to solve bilevel problems, this convex equivalent has very low computation time and is appropriate for real-time applications. Next, we compare the optimal solutions of the proposed personalized scheme and a uniform pricing scheme. We prove that, under the personalized pricing scheme, more prosumers contribute to the RTBM and the aggregator's cost is less. Finally, we verify the analytical results of this work by means of numerical case studies and simulations.

This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are parameters to be determined. The model of the reduced network is thereby obtained with parameterized system matrices, and then an edge weighting procedure is devised, aiming to select an optimal set of edge weights that minimizes the approximation error between the original and the reduced-order network models in terms of H2-norm. The effectiveness of the proposed method is illustrated by a numerical example.

In this paper, we treat extended balancing for continuous-time linear time-invariant systems, and we address the problem of structure-preserving model reduction of the subclass of port-Hamiltonian systems. We establish sufficient conditions to ensure that the reduced-order model preserves a port-Hamiltonian structure. Moreover, we show that the use of extended Gramians can be exploited to get a small error bound and, possibly, to preserve a physical interpretation for the reduced-order model., Comment: 32 pages, 13 figures. Submitted to IEEE Transactions on Automatic Control

In this paper, a novel distributed control strategy addressing a (feasible) psycho-social-physical welfare problem in islanded Direct Current (DC) smart grids is proposed. Firstly, we formulate a (convex) optimization problem that allows prosumers to share current with each other, taking into account the technical and physical aspects and constraints of the grid (e.g., stability, safety), as well as psycho-social factors (i.e., prosumers' personal values). Secondly, we design a controller whose (unforced) dynamics represent the continuous time primal-dual dynamics of the considered optimization problem. Thirdly, a passive interconnection between the physical grid and the controller is presented. Global asymptotic convergence of the closed-loop system to the desired steady-state is proved and simulations based on collected data on psycho-social aspects illustrate and confirm the theoretical results.

We consider the charge scheduling coordination of a fleet of plug-in electric vehicles, developing a hybrid decision-making framework for efficient and profitable usage of the distribution grid. Each charging dynamics, affected by the aggregate behavior of the whole fleet, is modelled as an inter-dependent, mixed-logical-dynamical system. The coordination problem is formalized as a generalized mixed-integer aggregative potential game, and solved via semi-decentralized implementation of a sequential best-response algorithm that leads to an approximated equilibrium of the game., Comment: Accepted to the 58th IEEE Conference on Decision and Control 2019 Nice

In this paper we propose a new passivity-based control technique for DC power networks comprising the so-called ZIP-loads, i.e., nonlinear loads with the parallel combination of unknown constant impedance (Z), current (I) and power (P) components. More precisely, we propose a novel passifying input and a storage function based on the so-called mixed potential function introduced by Brayton and Moser, leading to a novel passivity property with output port-variable equal to the first time derivative of the voltage. Differently from the existing results in the literature, where restrictive (sufficient) conditions on Z, P and the voltage reference are assumed to be satisfied, we establish a passivity property for every positive voltage reference and every type of load. Consequently, we develop a new decentralized passivity-based control scheme that is robust with respect to the uncertainty affecting the ZIP-loads., Comment: M. Cucuzzella and K. C. Kosaraju have given equivalent contribution

In this paper, our objective is to develop novel passivity based control techniques by introducing a new passivity concept named Krasovskii passivity. As a preliminary step, we investigate properties of Krasovskii passive systems and establish relations among four relevant passivity concepts including Krasovskii passivity. Then, we develop novel dynamic controllers based on Krasovskii passivity and based on extended shifted passivity.

This paper presents a new passivity property for distributed piezoelectric devices with integrable port-variables. We present two new control methodologies by exploiting the integrability property of the port-variables. The derived controllers have a Proportional-Integral (PI) like structure. Finally, we present the simulation results and in-depth analysis on the tuning gains explaining their transient and steady-state behaviors.

In this paper we introduce a new notion of passivity which we call Krasovskii's passivity and provide a sufficient condition for a system to be Krasovskii's passive. Based on this condition, we investigate classes of port-Hamiltonian and gradient systems which are Krasovskii's passive. Moreover, we provide a new interconnection based control technique based on Krasovskii's passivity. Our proposed control technique can be used even in the case when it is not clear how to construct the standard passivity based controller, which is demonstrated by examples of a Boost converter and a parallel RLC circuit.

In this paper, we present an empirical balanced truncation method for nonlinear systems with linear time-invariant input vector field components. First, we define differential reachability and observability Gramians. They are matrix valued functions of the state trajectory (i.e. the initial state and input trajectory) of the original nonlinear system, and it is difficult to find them as functions of the initial state and input. The main result of this paper is to show that for a fixed state trajectory, it is possible to compute the values of these Gramians by using impulse and initial state responses of the variational system. Therefore, balanced truncation is doable along the fixed state trajectory without solving nonlinear partial differential equations, differently from conventional nonlinear balancing methods. We further develop an approximation method, which only requires trajectories of the original nonlinear systems. Our methods are demonstrated by an RL network along a trajectory.

This work deals with the design of a robust and decentralized passivity-based control scheme for regulating the voltage of a DC microgrid through boost converters. A Krasovskii-type storage function is proposed and a (local) passivity property for DC microgrids comprising unknown 'ZIP' (constant impedance 'Z', constant current 'I' and constant power 'P') loads is established. More precisely, the input port-variable of the corresponding passive map is equal to the first-time derivative of the control input. Then, the integrated input port-variable is used to shape the closed loop storage function such that it has a minimum at the desired equilibrium point. Convergence to the desired equilibrium is theoretically analyzed and the proposed control scheme is validated through experiments on a real DC microgrid.

This paper investigates a model reduction problem for linear directed network systems, in which the interconnections among the vertices are described by general weakly connected digraphs. First, the definitions of pseudo controllability and observability Gramians are proposed for semistable systems, and their solutions are characterized by Lyapunov-like equations. Then, we introduce a concept of vertex clusterability to guarantee the boundedness of the approximation error and use the newly proposed Gramians to facilitate the evaluation of the dissimilarity of each pair of vertices. An clustering algorithm is thereto provided to generate an appropriate graph clustering, whose characteristic matrix is employed as the projections in the Petrov-Galerkin reduction framework. The obtained reduced-order system preserves the weakly connected directed network structure, and the approximation error is computed by the pseudo Gramians. Finally, the efficiency of the proposed approach is illustrated by numerical examples.

This paper deals with a class of Resistive-Inductive-Capacitive (RLC) circuits and switched RLC (s-RLC) circuits modeled in Brayton Moser framework. For this class of systems, new passivity properties using a Krasovskii's type Lyapunov function as storage function are presented. Consequently, the supply-rate is a function of the system states, inputs and their first time-derivatives. Moreover, after showing the integrability property of the port-variables, two simple control methodologies called output shaping and input shaping are proposed for regulating the voltage in RLC and s-RLC circuits. Global asymptotic convergence to the desired operating point is theoretically proved for both proposed control methodologies. Moreover, robustness with respect to load uncertainty is ensured by the input shaping methodology. The applicability of the proposed methodologies is illustrated by designing voltage controllers for DC-DC converters and DC networks.

This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of specifically selected generalized Gramians is implemented on the asymptotically stable part of the full-order network model, which leads to a reduced-order system preserving the passivity of each subsystem. Moreover, it is proven that there exists a coordinate transformation to convert the resulting reduced-order model to a state-space model of Laplacian dynamics. Thus, the proposed method simultaneously reduces the complexity of the network structure and individual agent dynamics, and it preserves the passivity of the subsystems and the synchronization of the network. Moreover, it allows for the a priori computation of a bound on the approximation error. Finally, the feasibility of the method is demonstrated by an example.