Research Projects

Energy-based modeling of physical systems is based on the fact that physical systems at a fundamental level can be decomposed into energy storage, dissipating, and routing elements. The Hamiltonian captures the total energy of the overall system, and the interconnection between different components (energy storage and energy dissipating elements) is written using variational principles. This leads to the so-called port-Hamiltonian (PH) modeling of systems. PH systems form an important modeling tool in almost all areas of system and control, particularly in network-based modeling of multi-physics multi-scale systems. They result in robust systems that can be easily interconnected. Any modification in the system (e.g., in power networks adding extra power lines into the network grid or removing some power lines from the network grid) can be interpreted as a structured perturbation (e.g. low-rank perturbation, perturbation without affecting the zero entries, or affecting only certain entries) of matrices or matrix pencils that linearize the nonlinear system. Our interest in this proposal is to study the effect of perturbations affecting various system properties such as stability, dissipativity, controllability, and observability. The loss of these properties can have catastrophic consequences regarding the safety and security of systems. Hence, it is useful for developing the structured perturbation analysis of PH systems that cause the system to preserve or violate system properties, like stability and dissipativity. The developed techniques will aid in providing design insights that could help build systems with guarantees of safety. In real-world applications, one uses mathematical models to simulate, control, or optimize a system or process. This mathematical model is infinite-dimensional (e.g., the determination of the electric or magnetic field associated with an electronic device) and is approximated by a finite element or finite difference model. The model is non-linear, and linearization is used to obtain a linear model. The model may also be obtained by a realization or system identification or result from a model order reduction procedure. These mathematical models, therefore, are typically inexact and contain uncertainties. Thus it is vital to study the following question: “How robust is a property of a dynamical system under perturbations of the coefficient matrices?”