Related papers: Extensive numerical study and circuitry implementa…
The phase diagram of a simple area-preserving map, which was motivated by the quantum dynamics of cold atoms, is explored analytically and numerically. Periodic orbits of a given winding ratio are found to exist within wedge-shaped regions…
Time-resolved photoemission spectroscopy provides a unique and direct way to explore the real-time nonequilibrium dynamics of electrons and holes. The formal theory of the spectral function evolution requires inclusion of electronic…
Stability analysis tools are essential to understanding and controlling any engineering system. Recently sum-of-squares (SOS) based methods have been used to compute Lyapunov based estimates for the region-of-attraction (ROA) of polynomial…
We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
Distributed consensus-based controllers for optimal secondary frequency regulation of microgrids and power systems have received substantial attention in recent years. This paper provides a Lyapunov-based proof that, under a time-scale…
Programmable quantum devices provide a platform to control the coherent dynamics of quantum wavefunctions. Here we experimentally realize adaptive monitored quantum circuits, which incorporate conditional feedback into non-unitary…
We study singularly perturbed systems that exhibit input-to-state stability (ISS) with fixed-time properties in the presence of bounded disturbances. In these systems, solutions converge to the origin within a time frame independent of…
While periodic responses of periodically forced dissipative nonlinear mechanical systems are commonly observed in experiments and numerics, their existence can rarely be concluded in rigorous mathematical terms. This lack of a priori…
Many complex systems can spontaneously oscillate under non-periodic forcing. Such self-oscillators are commonplace in biological and technological assemblies where temporal periodicity is needed, such as the beating of a human heart or the…
This paper introduces a novel approach to evaluating the asymptotic stability of equilibrium points in both continuous-time (CT) and discrete-time (DT) nonlinear autonomous systems. By utilizing indirect Lyapunov methods and linearizing…
In this work we identify and investigate a novel bifurcation in conserved systems. This secondary bifurcation stops active phase separation in its nonlinear regime. It is then either replaced by an extended, system-filling, spatially…
This letter addresses optimal controller design for periodic linear time-varying systems under unknown-but-bounded disturbances. We introduce differential Lyapunov-type equations to describe time-varying inescapable ellipsoids and define an…
In this paper, we present a framework for Stability Analysis of Systems of Coupled Linear Partial-Differential Equations. The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichelet,…
This paper develops a semidefinite-programming-based method for online feedback control of nonlinear systems using a state-dependent representation. We formulate sequences of time-varying SDPs whose optimal solutions jointly yield a…
This paper presents the cyber-physical system (CPS) of a numerical method (the widely-used Euler- Maruyama method) and establishes a foundational theory of the CPSs of numerical methods for stochastic differential equations (SDEs), which…
Model Predictive Control (MPC) is well understood in the deterministic setting, yet rigorous stability and performance guarantees for stochastic MPC remain limited to the consideration of terminal constraints and penalties. In contrast,…
Self-consistent chaotic transport is studied in a Hamiltonian mean-field model. The model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in…
It is well known that conservative mechanical systems exhibit local oscillatory behaviours due to their elastic and gravitational potentials, which completely characterise these periodic motions together with the inertial properties of the…
In this paper, we consider stochastic master equations describing the evolution of quantum spin-1/2 systems interacting with electromagnetic fields undergoing continuous-time measurements. We suppose that the initial states and the exact…
Computation, mechanics and materials merge in biological systems, which can continually self-optimize through internal adaptivity across length scales, from cytoplasm and biofilms to animal herds. Recent interest in such material-based…