相关论文: Nonlinear Feedback Shift Registers and Zech Logari…
We present a new method for the constraint-based synthesis of termination arguments for linear loop programs based on linear ranking templates. Linear ranking templates are parametrized, well-founded relations such that an assignment to the…
The paper presents an approach to the construction of stabilizing feedback for strongly nonlinear systems. The class of systems of interest includes systems with drift which are affine in control and which cannot be stabilized by continuous…
We propose a novel construction for the well-known prefer-max De Bruijn sequence, based on the cycle joining technique. We further show that the construction implies known results from the literature in a straightforward manner. First, it…
Nonlinear systems are capable of displaying complex behavior even if this is the result of a small number of interacting time scales. A widely studied case is when complex dynamics emerges out of a nonlinear system being forced by a simple…
We apply the iterative nonlinear programming method, previously proposed in our earlier work, to optimize Schur test functions and thereby provide refined upper bounds for the norms of integral operators. As an illustration, we derive such…
The exact nonlinear response of noninteracting (Bloch) electrons is examined within a nonequilibrium formalism on the infinite-dimensional hypercubic lattice. We examine the effects of a spatially uniform, but time-varying electric field…
For large nonlinear least squares loss functions in machine learning we exploit the property that the number of model parameters typically exceeds the data in one batch. This implies a low-rank structure in the Hessian of the loss, which…
Let $\widetilde{\alpha}$ be a length-$L$ cyclic sequence of characters from a size-$K$ alphabet $\mathcal{A}$ such that the number of occurrences of any length-$m$ string on $\mathcal{A}$ as a substring of $\widetilde{\alpha}$ is $\lfloor L…
Due to their simple construction, LFSRs are commonly used as building blocks in various random number generators. Nonlinear feedforward logic is incorporated in LFSRs to increase the linear complexity of the generated sequence. In this…
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…
Feedback optimization algorithms compute inputs to a system using real-time output measurements, which helps mitigate the effects of disturbances. However, existing work often models both system dynamics and computations in either discrete…
This paper proposes a unifying design framework for dynamic feedback controllers that track solution trajectories of time-varying generalized equations, such as local minimizers of nonlinear programs or competitive equilibria (e.g., Nash)…
Frequency-domain nonlinear wave mixing processes may be described either using response functions whereby the signal is generated after all interactions with the incoming fields, or in terms of scattering amplitudes where all fields are…
Different approaches to construct linear codes using skew polynomials can be unified by using the nonassociative algebras built from skew-polynomial rings by Petit.
We obtain some new properties of the signal generated by the Riemann zeta-function in this paper. Namely, we show the connection between the function $\zf$ and a nonlinear integral equation related to the Poisson-Lobachevsky integral.
The problem under consideration is the synthesis of a distributed controller for a nonlinear network composed of input affine systems. The objective is to achieve exponential convergence of the solutions. To design such a feedback law,…
We use the recently introduced concept of a Scaled Relative Graph (SRG) to develop a graphical analysis of input-output properties of feedback systems. The SRG of a nonlinear operator generalizes the Nyquist diagram of an LTI system. In the…
We use radial basis functions to model the input--output response of an electronic device. A new methodology for producing models that accuratly describe the response of the device over a wide range of operating points is introduced. A key…
In this work a combinatorial description is provided of a Faa di Bruno type Hopf algebra which naturally appears in the context of Fliess operators in nonlinear feedback control theory. It is a connected graded commutative and…
Shift registers/Primitive polynomials find applications in various branches of Mathematics, Coding Theory and Cryptography. Matrix analogues of primitive polynomials do exist. In this paper, an algorithmic approach to generating all such…