相关论文: On Sufficient Richness for Linear Time-Invariant S…

The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the…

This study is concerned with the problem of partial state estimation for linear time-invariant (LTI) distributed state-space systems. A necessary and sufficient condition is established in terms of a simple rank criterion involving the…

Permutation Entropy (PE) has been shown to be a useful tool for time series analysis due to its low computational cost and noise robustness. This has drawn for its successful application in many fields. Some of these include damage…

This paper develops a new framework for indirect statistical inference with guaranteed necessity and sufficiency, applicable to continuous random variables. We prove that when comparing exponentially transformed order statistics from an…

Based on the Fundamental Lemma by Willems et al., the entire behaviour of a Linear Time-Invariant (LTI) system can be characterised by a single data sequence of the system as long the input is persistently exciting. This is an essential…

Although persistent excitation is often acknowledged as a sufficient condition to exponentially converge in the field of adaptive parameter estimation, it must be noted that in practical applications this may be unguaranteed. Recently, more…

This paper proposes a new method to provide the exponential convergence of both the parameter and tracking errors of the composite adaptive control system without the persistent excitation (PE) requirement. Instead, the derived composite…

We formulate and prove in this report some sufficient conditions for exponential tightness (ET) of a family of independent identical distributed (i.i.d.) random fields (r.f.) (processes) in the space of continuous functions defined on…

In this paper, we provide a necessary and sufficient condition ensuring the property of exponential dichotomy for periodic linear systems of generalized differential equations. This condition allow us to revisit a recent result of…

Some necessary and sufficient conditions are obtained for the controllability and observability of a networked system with linear time invariant (LTI) dynamics. The topology of this system is fixed but arbitrary, and every subsystem is…

This paper develops necessary and sufficient conditions for the preservation of asymptotic convergence rates of deterministically and stochastically perturbed ordinary differential equations with regularly varying nonlinearity close to…

One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…

A central question in verification is characterizing when a system has invariants of a certain form, and then synthesizing them. We say a system has a $k$ linear invariant, $k$-LI in short, if it has a conjunction of $k$ linear (non-strict)…

For constrained linear systems with bounded disturbances and parametric uncertainty, we propose a robust adaptive model predictive control strategy with online parameter estimation. Constraints enforcing persistently exciting closed loop…

In this paper, a concurrent learning based adaptive observer is developed for a class of second-order linear time-invariant systems with uncertain system matrices. The developed technique yields an exponentially convergent state estimator…

In this paper, an attack-resilient estimation algorithm is presented for linear discrete-time stochastic systems with state and input constraints. It is shown that the state estimation errors of the proposed estimation algorithm are…

We present necessary conditions for monotonicity, in one form or another, of fixed point iterations of mappings that violate the usual nonexpansive property. We show that most reasonable notions of linear-type monotonicity of fixed point…

The problem of estimating a random vector x from noisy linear measurements y = A x + w with unknown parameters on the distributions of x and w, which must also be learned, arises in a wide range of statistical learning and linear inverse…

In this paper, we give a general time-varying parameter model, where the multidimensional parameter possibly includes jumps. The quantity of interest is defined as the integrated value over time of the parameter process $\Theta = T^{-1}…

How many parameters are required for a model to execute a given task? It has been argued that large language models, pre-trained via self-supervised learning, exhibit emergent capabilities such as multi-step reasoning as their number of…