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When the system is linear, why should learning be nonlinear? Linear dynamical systems, the analytical backbone of control theory, signal processing and circuit analysis, have exact closed-form solutions via the state transition matrix. Yet…
This Ph.D. thesis is divided in two parts. The first one concerns the equilibrium properties of glassy systems. Some aspects of the phenomenology of glasses and of theories attempting to describe them are reviewed in chapter 1. A study of…
A collection of converse theorems for integral quadratic constraints (IQCs) is established for linear time-invariant systems. It is demonstrated that when a system interconnected in feedback with an arbitrary system satisfying an IQC is…
Radical-ion-pair reactions were recently shown to manifest a host of non-trivial quantum effects accounted for by quantum measurement theory. An alternative approach purporting to describe the fundamental quantum dynamics of spin-selective…
We show explicitly the entropy reduction from a detailed fluctuation theorem for the general stochastic system driven by nonequilibrium process under feedback control. The effect of interaction of the feedback controller with the system is…
A novel strategy is proposed for the coupling of field and circuit equations when modeling power devices in the low-frequency regime. The resulting systems of differential-algebraic equations have a particular geometric structure which…
State space is widely used for modeling power systems and analyzing their dynamics but it is limited to representing causal and proper systems in which the number of zeros does not exceed the number of poles. In other words, the system…
Basic multimode impedance analysis grounded in the availability of nonequilibrium charge carriers and their retarded path towards equilibrium is used to access the inadequacy of equivalent circuits in nonlinear systems with inherent memory.…
In this paper, we design a symbolic output feedback controller of a cyber-physical system (CPS). The physical plant is modeled by an infinite transition system. We consider the situation that a finite abstracted system of the physical…
Reflection positivity (RP) is a property of Gibbs measures exhibited by a class of lattice spin systems that include the Ising, Potts and Heisenberg models. The RP property is useful because of its two basic consequences: infrared bound and…
Intracavity frequency-doubled solid-state lasers exhibit intensity fluctuations of their light output, which are cause by nonlinear dynamical processes. Up to now, there are different solutions to this problem, but they reduce the output…
It is argued that a realistic interpretation of quantum mechanics is possible and useful. Current interpretations, from Copenhagen to many worlds are critically revisited. The difficulties for intuitive models of quantum physics are pointed…
As bulk synchronous generators in the power grid are replaced by distributed generation interfaced through power electronics, inertia is removed from the system, prompting concerns over grid stability. Different metrics are available for…
Reciprocity is a fundamental symmetry property observed across many physical domains, including acoustics, elasticity, electromagnetics, and thermodynamics. In systems and control theory, it provides key insights into the internal structure…
Humans have a remarkable ability to use physical commonsense and predict the effect of collisions. But do they understand the underlying factors? Can they predict if the underlying factors have changed? Interestingly, in most cases humans…
The theory of feedback integrators is extended to handle mechanical systems with nonholonomic constraints with or without symmetry, so as to produce numerical integrators that preserve the nonholonomic constraints as well as other conserved…
Nonlinear real-time response of interacting particles is studied on the example of a one-dimensional tight-binding model of spinless fermions driven by electric field. Using equations of motion and numerical methods we show that for a…
Numerical modelling of several coupled passive linear dynamical systems (LDS) is considered. Since such component systems may arise from partial differential equations, transfer function descriptions, lumped systems, measurement data, etc.,…
We analyze experimental data obtained from an electrical circuit having components at different temperatures, showing how to predict its response to temperature variations. This illustrates in detail how to utilize a recent linear response…
Due to the rapid developments in synchronized measurement technologies, there exist enormous opportunities to attenuate disturbances in future power grids with high penetration of renewables and complex load demands. To that end, this paper…