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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., ECC 2021- Accepted version with minor changes. Fixed a minor gramatic typo in experiments section

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., 4 pages, 1 figure, This work is accepted as a Late-Breaking result at the IFAC World Congress 2020

In this paper we propose a new distributed passivity-based control scheme, achieving proportional (fair) current sharing and average voltage regulation in Direct Current (DC) power networks, with an arbitrary topology. The considered DC network is composed of several Distributed Generation Units (DGUs) interconnected through resistive-inductive power lines. Each DGU includes a generic energy source that supplies an unknown constant impedance load through a DC-DC buck converter. The proposed distributed control scheme achieves current sharing and average voltage regulation, independently of the initial condition of the controlled network, facilitating Plug-and-Play capabilities. Moreover, the proposed control strategy exploits a communication network to achieve current sharing using a consensuslike protocol. Global convergence to a desired steady state is proven and simulations show satisfactory performance.

This paper studies a moment matching model reduction method for second-order network systems. For a given complex second-order network system, our goal is to find a reduced second-order network system that achieves moment matching. Firstly, the original second-order network system is split into an asymptotically stable subsystem and an average subsystem. Then, moment matching approach is implemented to reduce the dimension of the asymptotically stable subsystem. The resulting reduced-order model is combined with the average subsystem, leading to a reduced second-order system preserves the semistability. Subsequently, a specific coordinate transform allows for the reduced-order model to be converted to a complete network. A mass-spring-damper network demonstrates the effectiveness of the proposed method.

In this paper, a novel distributed control strategy achieving (feasible) current sharing and voltage regulation in Direct Current (DC) microgrids is proposed. Firstly, the (convex) optimization problem is formulated, with the microgrid's steady state equations and/or desired objectives as feasible set. Secondly, we design a controller, the (unforced) dynamics of which represent the continuous time primal-dual dynamics of the considered optimization problem. Then, a passive interconnection between the physical plant and the controller is presented.

In this note we address the problem of model reduction of a particular class of linear systems, namely, the linear port-Hamiltonian (PH) systems. Furthermore, we explore the preservation of the PH structure in the reduced model. Towards this end, we adopt the balanced truncation approach to reduced the order of the model, in particular, we study the use of extended Gramians to balance the linear PH systems. The latter provides degrees of freedom to impose a desired structure, in this case a PH one, to the reduced model. Moreover, for balanced truncation using extended Gramians, the error bound is well-known and is given in terms of the Hankel singular values of the truncated state.

We present a distributed control law for a group of agents that solves the problem of formation control with obstacle avoidance and that can be combined with a coordinated group stabilization control law. In particular, we consider a control law that is given by a linear combination of distributed formation, distributed obstacle avoidance and centralized group motion control laws. Simulation results show the effectiveness of our proposed control law.

In this paper, we study robust cooperative output regulation problems for a directed network of Lur'e systems that consist of a nominal linear dynamics with an unknown static nonlinearity around it through negative feedback. We assume that the linear part of each agent is identical, but the nonlinearities are allowed to be different for distinct agents. In this sense, the network is heterogeneous. As is common in the context of Lur'e systems, the unknown nonlinearities are assumed to be sector bounded within one given sector. The interconnection graph among these agents is assumed to contain a directed spanning tree. Similar to classical output regulation problems, there is a virtual exosystem generating a reference signal in which all the agents are required to track cooperatively. Our designed distributed dynamic state/output feedback protocol makes a copy of the reference signal at each agent asymptotically, and then the robust cooperative output regulation problem becomes a robust tracking problem that can be handled by each agent via local information. It turns out that our cooperative protocols are fully distributed. Sufficient conditions on the existence of output synchronization protocols are given along with some discussions on these conditions. Finally, two simulation examples illustrate our design. Copyright (c) 2016 John Wiley & Sons, Ltd.

In the intuitive modelling of the power network, the generators and the loads are located at different subset of nodes. This corresponds to the so-called structure preserving model which is naturally expressed in terms of differential algebraic equations (DAE). The algebraic constraints in the structure preserving model are associated with the load dynamics. Motivated by the fact the presence of the algebraic constraints hinders the analysis and control of power networks, several aggregated models are reported in the literature where each bus of the grid is associated with certain load and generation. The advantage of these aggregated models is mainly due to the fact that they are described by ordinary differential equations (ODE) which facilitates the analysis of the network. However, the explicit relationship between the aggregated model and the original structure preserved model is often missing, which restricts the validity and applicability of the results. Aiming at simplified ODE description of the model together with respecting the heterogenous structure of the power network has endorsed the use of Kron reduced models; see e.g. [2]. In the Kron reduction method, the variables which are exclusive to the algebraic constraints are solved in terms of the rest of the variables. This results in a reduced graph, the (loopy) Laplaican matrix of which is the Schur complement of the (loopy) Laplacian matrix of the original graph. By construction, the Kron reduction technique restricts the class of the applicable load dynamics to linear loads. The algebraic constraints can also be solved in the case of frequency dependent loads where the active power drawn by each load consists of a constant term and a frequencydependent term [1],[3]. However, in the popular class of constant power loads, the algebraic constraints are “proper”, meaning that they are not explicitly solvable. In this talk, first we revisit the Kron reduction method for the linear case, where the Schur complement of the Laplacian matrix (which is again a Laplacian) naturally appears in the network dynamics. It turns out that the usual decomposition of the reduced Laplacian matrix leads to a state space realization which contains merely partial information of the original power network, and the frequency behavior of the loads is not visible. As a remedy for this problem, we introduce a new matrix, namely the projected pseudo incidence matrix, which yields a novel decomposition of the reduced Laplacian. Then, we derive reduced order models capturing the behavior of the original structure preserved model. Next, we turn our attention to the nonlinear case where the algebraic constraints are not readily solvable. Again by the use of the projected pseudo incidence matrix, we propose explicit reduced models expressed in terms of ordinary differential equations. We identify the loads embedded in the proposed reduced network by unveiling the conserved quantity of the system.

In PowerMatching City, the leading Dutch smart grid project, 40 households participated in a field laboratory designed for sustainable living. The participating households were equipped with various decentralized energy sources (PV and micro combined heat-power units), hybrid heat pumps, smart appliances, smart meters, and an in-home display. Stabilization and optimization of the network was realized by trading energy on the market. To reduce peak loads on the smart grid and to be able to make optimal use of the decentralized energy sources, two energy services were developed jointly with the end users: Smart Cost Savings enabled users to keep the costs of energy consumption as low as possible, and Sustainable Together enabled them to become a sustainable community. Furthermore, devices could be controlled automatically, smartly, or manually to optimize the energy use of the households. Quantitative and qualitative studies were conducted to provide insight into the experiences and behaviours of end users. In this chapter, these experiences and behaviours are described. The chapter argues that end users: (1) prefer to consume self-produced energy, even when it is not the most efficient strategy to follow, (2) prefer feedback on costs over feedback on sustainability, and (3) prefer automatic and smart control, even though manual control of appliances felt most rewarding. Furthermore, we found that experiences and behaviours were fully dependent on trust between community members, and on trust in both technology (ICT infrastructure and connected appliances) and the participating parties.