Port-Hamiltonian Modeling for Control

This article provides a concise summary of the basic ideas and concepts in port-Hamiltonian systems theory and its use in analysis and control of complex multiphysics systems. It gives special attention to new and unexplored research directions and relations with other mathematical frameworks. Emergent control paradigms and open problems are indicated, including the relation with thermodynamics and the question of uniting the energy-processing view of control, as emphasized by port-Hamiltonian systems theory, with a complementary information-processing viewpoint.</p

Reciprocity of nonlinear systems

One of the key contributions of the 1972 seminal paper by Willems was the analysis of symmetry (also called reciprocity) of input-state-output systems, both from an external (input-output) and internal (state) point of view. The developed theory also included the combination of reciprocity with passivity, and the consideration of relaxation systems, which are passive reciprocal systems without any oscillatory behavior. The paper was motivated from a fundamental system-theoretic point of view (how is external structure reflected into internal structure), as well as by a wide range of application areas, including electrical network synthesis, thermodynamics, and viscoelastic materials. On the other hand, the obtained results are for linear systems, and the extension to the nonlinear case, even for subclasses of nonlinear systems, is far from trivial. The present paper aims at taking some steps into this direction.Comment: 31 page

Differential–algebraic systems with dissipative Hamiltonian structure

Different representations of linear dissipative Hamiltonian and port-Hamiltonian differential–algebraic equations (DAE) systems are presented and compared. Using global geometric and algebraic points of view, translations between different representations are presented. Characterizations are also derived when a general DAE system can be transformed into one of these structured representations. Approaches for computing the structural information and the described transformations are derived that can be directly implemented as numerical methods. The results are demonstrated with a large number of examples.</p

Consensus dynamics in distribution networks and nonlinear multi-agent systems

In this thesis we first consider a basic model of a dynamical distribution network, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and outflows. In order to achieve the output agreement among the vertices, we employ distributed PI controllers which regulate the flow inputs. Then we consider the flow constraint and storage constraint cases respectively. For the flow constraint case, we derive sufficient and necessary conditions for output agreement, which only depend on the structure of the network and the flow constraint intervals. For the storage constraint case, we design a PI controller with state-based saturation for the flows to achieve the output agreement and to keep the storage constraint being satisfied all the time. Second we study consensus problems for multi-agent systems defined on directed graphs where the consensus dynamics involves nonlinear and discontinuous functions. Sufficient (and necessary in some cases) conditions, involving the nonlinear functions and the topology of the underlying graph, for the agents to converge to static consensus are provided. For a special case, namely the multi-agent system defined on a strongly connected graph with continuous functions, we show the convergence by using a port-Hamiltonian formulation

Energy-based analysis and control of power networks and markets:Port-Hamiltonian modeling, optimality and game theory

This research studies the modeling, control and optimization of power networks. A unifying mathematical approach is proposed for the modeling of both the physical power network as well as market dynamics. For the physical system, several models of varying complexity describing the changes in frequency and voltages are adopted. For the electricity market, various dynamic pricing algorithms are proposed that ensure a optimal dispatch of power generation and demand (via flexible loads). Such pricing algorithms can be implemented in real-time and using only local information that is available in the network (such as the frequency). By appropriately coupling the physical dynamics with the pricing algorithms, stability of the combined physical-economical system is proven. This in particular shows how real-time dynamic pricing can be used as a control method to achieve frequency regulation and cost efficiency in the network