Modeling and Control of Complex Physical Systems

Stabilization of infinite dimensional port-Hamiltonian systems by nonlinear dynamic boundary control

“…It has been shown that distributed port-Hamiltonian systems encompass a large class of physical systems, including mechanical, electrical, electro-mechanical, hydraulic and chemical systems to mention some. See Duindam et al (2009) for an extensive exposition and a large list of references. Regarding the extension of the Hamiltonian formulation to stabilizing control of BCS, in the 1D linear case it gave rise to the definition of boundary control portHamiltonian systems (BC-PHS) (Le Gorrec et al, 2004) and allowed to parametrize, by using simple matrix conditions, the boundary conditions that define a well-posed problem .…”

Port-Hamiltonian Formulation of Systems With Memory

“…Although the general structure of a port-Hamiltonian system possesses rich mathematical properties, we will only highlight those characteristics that are central in the expositions throughout the paper. The interested reader is referred to [17] for a basic introduction, and to [7] for a comprehensive summary of the developments of the port-Hamiltonian framework over the past two decades. Section III reviews the basic properties of the memristor, meminductor, and memcapacitor, followed by their characterization in the port-Hamiltonian framework in Section IV.…”

Structure-preserving model reduction for nonlinear port-Hamiltonian systems

“…If the core dynamics of subsystem components are described by variational principles (e.g., least-action or virtual work), the aggregate system model typically has structural features that characterize it as a port-Hamiltonian system. While greater generality is both possible and useful (see, in particular, the review article [28], and the monographs [8] and [30]), it will suffice to consider realizations of finite-dimensional nonlinear port-Hamiltonian (nlph) systems that appear as:ẋ = (J − R) ∇ x H(x) + Bu(t) y = B T ∇ x H(x), (1.1) where x ∈ R n is the n-dimensional state vector; H : R n → [0, ∞) is a continuously differentiable scalar-valued vector function -the Hamiltonian, describing the internal energy of the system as a function of state; J = −J T ∈ R n×n is the structure matrix describing the interconnection of energy storage elements in the system; R = R T ≥ 0 is the n × n dissipation matrix describing energy loss in the system; and, B ∈ R n×m is the port matrix describing how energy enters and exits the system. We will always assume that the Hamiltonian is bounded below and so without loss of generality, strictly positive, H(x) > 0 for all x.…”