Related papers: Nonlinear dissipation can combat linear loss

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…

A mathematical model describing the initial stage of the capture into autoresonance for nonlinear oscillating systems with combined parametric and external excitation is considered. The solutions with unboundedly growing amplitude and…

A system that violates detailed balance evolves asymptotically into a nonequilibrium steady state with non-vanishing currents. Analogously, when detailed balance holds at any instant of time but the system is driven through time-periodic…

Full coherent control and generation of superpositions of the quantum harmonic oscillator are not only of fundamental interest but are crucial for applications in quantum simulations, quantum-enhanced metrology and continuous-variable…

Cat states, with their unique phase-space interference properties, are ideal candidates for understanding fundamental principles of quantum mechanics and performing key quantum information processing tasks. However, they are highly…

In this paper, I derive a closed expression for how precisely a small-scaled system can follow a pre-defined trajectory, while keeping its dissipation below a fixed limit. The total amount of dissipation is approximately inversely…

The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…

For a general class of dynamical systems (of which the canonical continuous and uniform discrete versions are but special cases), we prove that there is a state feedback gain such that the resulting closed-loop system is uniformly…

Nonlinear contact dynamics are widely regarded as intrinsically nonlinear systems whose behaviour depends strongly on geometry and impact conditions. Here we show that any one-dimensional conservative contact system satisfying monotone…

This paper addresses the problem of robust process and sensor fault reconstruction for nonlinear systems. The proposed method augments the system dynamics with an approximated internal linear model of the combined contribution of known…

We present a new direct adaptive control approach for nonlinear systems with unmatched and matched uncertainties. The method relies on adjusting the adaptation gains of individual unmatched parameters whose adaptation transients would…

We study a nonlinear system made up of an elliptic equation of blended singular/degenerate type and Poisson's equation with a lowly integrable source. We prove the existence of a weak solution in any space dimension and, chiefly, derive an…

We design nonlinear and adaptive linear model-predictive control (MPC) techniques to minimize operational costs of compressor-actuated dynamics in natural gas pipeline networks. We establish stability of the local linear system and derive…

This paper presents a technique to drive the state of a constrained nonlinear system to a specified target state in finite time, when the system suffers a partial loss in control authority. Our technique builds on a recent method to control…

This paper deals with the data-driven synthesis of dissipative linear systems in discrete time. We collect finitely many noisy data samples with which we synthesise a controller that makes all systems that explain the data dissipative with…

Error correction is essential for modern computing systems, enabling information to be processed accurately even in the presence of noise. Here, we demonstrate a new approach which exploits an error correcting phase that emerges in a system…

We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our conditions are of a very general form and provided that the nonlinear perturbations are…

Combining analytical and numerical methods, we study within the framework of the homogeneous non-linear Boltzmann equation, a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the new…

We show that useful non-instantaneous nonlinear phase shifts can be obtained from cascaded quadratic processes in the presence of group velocity mismatch. The two-field nature of the process permits responses that can be effectively…

The paper considers the design of a nonlinear dissipative impulsive observer based on non-periodic discrete-time measurements. Sufficient conditions are derived for (i) exponential convergence of the observer in absence of measurement…