Related papers: ARX modeling of unstable linear systems
We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…
The arterial system dynamically loads the heart through changes in arterial compliance. The pressure-volume relation of arteries is known to be nonlinear, but arterial compliance is often modeled as a constant value, due to ease of…
This paper is directed towards the problem of learning nonlinear ARX models based on system input--output data. In particular, our interest is in learning a conditional distribution of the current output based on a finite window of past…
In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line…
An overdamped system with a linear restoring force and two multiplicative colored noises is considered. Noise amplitudes depend on the system state $x$ as $x$ and $|x|^{\alpha}$. An exactly soluble model of a system is constructed due to…
The problem of remotely stabilizing a noisy linear time invariant plant over a Gaussian relay network is addressed. The network is comprised of a sensor node, a group of relay nodes and a remote controller. The sensor and the relay nodes…
We present a new method for locating unstable periodic points of one dimensional chaotic maps. This method is based on order statistics. The densities of various maxima of the iterates are discontinuous exactly at unstable periodic points…
In this paper, we propose a novel framework for disturbance rejection in a class of nonautonomous nonlinear systems affected by trigonometric-polynomial disturbances. The core of our approach is the design of a canonical internal model that…
In this study, we propose new global stabilization approaches for a class of polynomial systems in both model-based and data-driven settings. The existing model-based approach guarantees global asymptotic stability of the closed-loop system…
We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…
The Kaczmarz method is an iterative algorithm for solving systems of linear equations Ax=b. Theoretical convergence rates for this algorithm were largely unknown until recently when work was done on a randomized version of the algorithm. It…
In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis…
Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…
We use series expansions to study dynamics of equilibrium and non-equilibrium systems on networks. This analytical method enables us to include detailed non-universal effects of the network structure. We show that even low order…
The paper introduces a novel methodology for the identification of coefficients of switched autoregressive linear models. We consider the case when the system's outputs are contaminated by possibly large values of measurement noise. It is…
In theories with unstable particles, unitarity is satisfied by the inclusion of only stable states in unitarity sums. Hence unitarity cuts are not to be taken through unstable particles. This raises a challenge to the generalized unitarity…
We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…
We consider the problem of stabilization of a linear system, under state and control constraints, and subject to bounded disturbances and unknown parameters in the state matrix. First, using a simple least square solution and available…