An up-to-date survey of the theory of port-Hamiltonian systems is given, emphasizing novel developments and relationships with other formalisms. Port-Hamiltonian systems theory yields a systematic framework for network modeling of multi-physics systems. Examples from different areas show the range of applicability. While the emphasis is on modeling and analysis, the last part provides a brief introduction to control of port-Hamiltonian systems.

In this paper, a novel distributed control algorithm for current sharing and voltage regulation in DC microgrids is proposed. The DC microgrid is composed of several distributed generation units, including buck converters and current loads. The considered model permits an arbitrary network topology and is affected by an unknown load demand and modeling 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 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.

In this paper we propose a model reduction method for biochemical reaction networks governed by a variety of reversible and irreversible enzyme kinetic rate laws, including reversible Michaelis-Menten and Hill kinetics. The method proceeds by a stepwise reduction in the number of complexes, defined as the left and right-hand sides of the reactions in the network. It is based on the Kron reduction of the weighted Laplacian matrix, which describes the graph structure of the complexes and reactions in the network. It does not rely on prior knowledge of the dynamic behaviour of the network and hence can be automated, as we demonstrate. The reduced network has fewer complexes, reactions, variables and parameters as compared to the original network, and yet the behaviour of a preselected set of significant metabolites in the reduced network resembles that of the original network. Moreover the reduced network largely retains the structure and kinetics of the original model.

Since the 1970s, contact geometry has been recognized as an appropriate framework for the geometric formulation of thermodynamic systems, and in particular their state properties. More recently it has been shown how the symplectization of contact manifolds provides a new vantage point; enabling, among other things, to switch easily between the energy and entropy representations of a thermodynamic system. In the present paper, this is continued towards the global geometric definition of a degenerate Riemannian metric on the homogeneous Lagrangian submanifold describing the state properties, which is overarching the locally-defined metrics of Weinhold and Ruppeiner. Next, a geometric formulation is given of non-equilibrium thermodynamic processes, in terms of Hamiltonian dynamics defined by Hamiltonian functions that are homogeneous of degree one in the co-extensive variables and zero on the homogeneous Lagrangian submanifold. The correspondence between objects in contact geometry and their homogeneous counterparts in symplectic geometry, is extended to the definition of port-thermodynamic systems and the formulation of interconnection ports. The resulting geometric framework is illustrated on a number of simple examples, already indicating its potential for analysis and control.

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 turbine-governor dynamics. The turbine-governor dynamics suggest the design of a sliding manifold such that the turbine-governor system enjoys a suitable passivity property, once the sliding manifold is attained. This paper offers a new perspective on OLFC by means of SM control, and in comparison with the existing literature, we relax required dissipation conditions on the generation side and assumptions on the system parameters.